I was wondering whether the pair 頼む and 頼もしい are a more or less singular event - or is there a pattern, like e.g.
飲む → 飲もしい （“drinkable“)??
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It’s always interesting to dig around when this type of question pops up because I often get surprised by relative apparent things I have never thought of.
I’m not gonna say that they is a pattern as you describe it because I just don’t know. But, I found these two links that might put some info on the table
Human emotions or perceptual state (ooh moment)
Entire answer was interesting but partial clarification is covered under irregular vowel shift
Hope it’s to some help
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Thanks - that definitely helped.
It is really great to be on a forum where people are so forthcoming - makes learning so much more fun.
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You can’t do all words, but there is a trend on some words.
疑う
疑わしい
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Almost all of the あしい endings indicate some kind of feeling based on the observer that (A) is exhibiting a trait that is typical of what is being described. らしい itself is an example of this.
アッシャーらしい (Typical of Asher)
疑わしい (Typical of something doubtful)
好ましい (Typical of something liked/desirable)
喜ばしい (Typical of something joyous)
輝かしい (Typical of something radiant)
Note that あしい is outside of the kanji in each of these. When the ending is しい itself (regardless of what is inside the kanji), the meaning is much more based on the speaker’s opinion, rather than the innate qualities of what is being described.
Basically -
あしい - Shows a trait that one would expect of something that is (A).
しい - Is (A) according to the speakers current feeling.
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How did you come to know this? Do you have a specific resource you care to share? 
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Just seeing them all used many times. It is a personal observation that you can take with a grain of salt, and confirm/deny based on your own conclusion. In my observation, all the あ based sounds refer to the way something exists.
If we take a few random sentences from takoboto.
ビルが来るかどうかは疑わしい。
It is doubtful whether Bill will come. (Bill himself coming is a doubtful thing, regardless of any speaker’s opinion)
彼の欠点にもかかわらずサムはとても好ましい人物だ。
Regardless of Sam’s shortcomings, he is still a really likable fellow.
(Sam himself is a likable person, regardless of any speaker’s opinion)
その軍団は戦闘中多くの輝かしい作戦に従事した。
That unit was involved in a lot of brilliant strategies during the war.
(The plans themselves exhibited brilliance, regardless of any speaker’s opinion)
外国語を学ぶことは楽しい。
Learning a foreign language is fun.
(The fun involved in learning relies on the speakers viewpoint, not the innate qualities of learning)
I think the more you are exposed to it, the more obvious it gets, but I’ll let you be the judge 
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Please feel free to chuck a few random adjectives at me if you want some more examples. I literally just grabbed what was already in this thread.
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Like @Asher said and you guys have noticed there is a pattern to this.
Take a tea and start reading if you are curious. 
Long time ago, in Japanese nominals (nouns) were used as adjectives, to describe other nouns. They wer simply put before modified noun. Verbs were also created by attaching certain auxiliaries to nominals (and this is probably answer to the original question). From certain perspective, Japanese adjectives can be considered to be a specialized form of verbs.
Eventually Japanese started adding し to those nouns, creating first adjectives. Some of those also gave birth to some static verbs, that’s why we have some static verbs and adjectives that sound similar.
Example: 大人 - “adult” => 大人し - “mature”
The form ending with し was 終止形, the form only used at the end of the sentence (and not in all circumstances).
Coming back to **し - the first adjectives were the ones that represented observable physical condition. **
For example: 清し (‘clean’, ‘clear’).
Those adjectives are called く adjectives (due to their 連用形 form)
The other group which appeared later and was less numerous (originally, because eventually, they have grown in number) also ended with し in their 終止形. They were more subjective, and described feelings and so on.
For example 美し (‘lovely’)
Those adjectives are called しく adjectives (due to their 連用形 form)
However, the major difference was in conjugation:
| Conugation | 清し (く adjective) | 美し(しく adjective) |
|---|---|---|
| 未然形（imperfective form (things that not happened), nai stem) | - | - |
| 連用形(conjunctive form (connects), masu stem) | 清く | 美しく |
| 終止形(predicative form, ending form) | 清し | 美し |
| 連体形(attributive form, noun modifying form) | 清き | 美しき |
| 已然形(realis form (thing that happened, used with ば and ども as in けれども) | 清けれ | 美しけれ |
| 命令形(imperative form) used for orders | - | - |
As you can see, the major difference was that in the case of しく adjective, し stayed in all conjugations, while in く adjectives case it was replaced.
Examples: なし(ない)、べし(nowadays べきだ)、ごとし,
To those conjugations various auxiliary verbs were added. Those auxiliaries were for example む、なる and some other.
Unfold if you are curious about lack of the imperative and irrealis forms
You can also notice, that both did not have an imperative form or imperfective form. For that purpose verb, あり (nowadays ある) had been added to 連用形 which gave くあり ending. This was shortened to かり and conjugated for the missing forms:
| Conugation | 清し (く adjective) | 美し(しく adjective) |
|---|---|---|
| 未然形 | 清から | 美しから |
| 連用系 | 清かり | 美しかり |
| 終止形 | - | - |
| 連体形 | 清かる | 美しかる |
| 已然形 | - | - |
| 命令形 | 清かれ | 美しかれ |
Eventually, い-sound change happened in attributive form, and the k in き was dropped. (Similar change happened to some verbs like ござります->ございます)
So:
| old 連体形 | 清き | 美しき |
|---|---|---|
| new 連体形 | 清い | 美しい |
And this is from where we have the modern forms, eventually, the 終止形 stopped being used, and the 連体形 (attributive form) took its role which made it possible to use the same form to when both modifying nouns and at the end of the sentence.
And this is why some adjectives ending with しい describe feelings more often, and the ones just ending with い describe some observable phenomenons
Of course, some adjectives retained some of their original conjugations, like ごとし.
You can also see sometimes なき (old attributive form) being used instead of ない.
At example below が works as a nominalizer, just like modern の.
Example:
サービス業のマネージャーを任されている私にとって、休日などはあって**なきが如し。
For me, who has been entrusted as the manager of the service sector, something like days off are virtually nonexistent.
As you can see, originally Japanese
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Interesting! I had long wondered if there was some connection between い-adjectives and the く-to-い conjugation of godan く verbs, and from what I’ve read so far of your post, it seems that there is. Looks like they started as く(and しく) verbs and their い-form ( 連用形?) became what we know today as い-adjectives?! (Or something? Maybe I’m a little confused; if so, that’s okay; mainly I’m just interested in if there is a connection or not, not necessarily the precise relationship…) In any case, cool!
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Holy crow, I just realized this also makes sense of why past-tense い-adjectives are conjugated as かった! It’s because we’re actually conjugating a kind of a く verb (though not the same way as a く godan verb), from う-ending to あ-ending, into か, and somehow that goes to かった for past tense! Crazy connections just a little historical insight can make!
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