I'm just throwing this up against the wall because I don't know anything at all about that vintage & the schematics that I do have, such as most of them are, only cover from '97 through '04 (& except for '03 they are incomplete) but it sounds like there must be a combination flasher or switch that covers the functions you listed & it must have gone bad. That's just a total guess though.
You really need a schematic (& maybe someone with one for that year/period will get in on this) to trace out the circuits. Haynes does have schematics in back of their books, but I can see no rhyme or reason to which they include & which they don't. First choice would be the FSM for your year; you might find one on ebay for reasonable. Also, I recently read a post by someone that said if you go to Autozone's site you can get free schematics online. I've never personally tried that, but maybe give that a look.
You really need a schematic (& maybe someone with one for that year/period will get in on this) to trace out the circuits. Haynes does have schematics in back of their books, but I can see no rhyme or reason to which they include & which they don't. First choice would be the FSM for your year; you might find one on ebay for reasonable. Also, I recently read a post by someone that said if you go to Autozone's site you can get free schematics online. I've never personally tried that, but maybe give that a look.