Whilst there aren't many online resources for this sort of thing, there are very extensive paper resources. I highly recommend that you get either the NHK日本語発音アクセント辞典 or the 新明解日本語アクセント辞典 if you have questions beyond these two conjugations; you can figure out the tables even with very limited Japanese.
Essentially, 〜ない and 〜たい are actually separate words that attach to various stem forms of said verb (imperfective and continuative, respectively). Although they are separate units, they cannot be stand-alone words and are known as auxiliaries (助動詞). These auxiliaries conjugate differently to the verbs that they are attached to, which is why it seems to turn it into an adjective, as you put it.
There are a pretty limited number of pitch accent patterns for auxiliaries, but there is no way to know which pattern each follows without looking it up. Note that any pattern does not apply to conjugations of 〜ない and 〜たい, such as 〜なかった and 〜たかった, which have independent patterns and also can be looked up in these conjugation tables.
According to the NHK日本語発音アクセント辞典, where ○○ represents the verb stem and ●● represents the auxiliary:
〜ない [Type 3.1]
[○○↘●●] When connecting to a downstep-type verb (atamadama, nakadaka, or odaka), the downstep is inserted between the two units. e.g. 帰る: かえる【HLL】 becomes かえらない【LHHLL】
[○○●●→] When connected to a heiban-type verb, the entire word becomes heiban. e.g. 買う: かう【LH】becomes かわない【LHHH】
〜たい [Type 2]
[○○●↘●] When connecting to a downstep-type verb, the downstep is inserted after the first mora of the auxiliary. e.g. 帰る: かえる【HLL】 becomes かえりたい【LHHHL】
[○○●●→] When connected to a heiban-type verb, the entire word becomes heiban. e.g. 買う: かう【LH】becomes かいたい【LHHH】. However, for 〜たい specifically, the downstep-type verb rule [○○●↘●] has also become acceptable as a variant for heiban verbs. e.g. 買う: かう【LH】becomes かいたい【LHHL】