What should you check next on a 1995 Eclipse GSX the turn signals do not work and the fuses are good?

Sounds like one of 2 things.

Check the flasher unit and all of its connections. Make sure that the connections are good. You may want to remove the flasher unit and then re-insert it.

Then check for the wiring - like grounding, etc.

Finally check the fuses again - there are fuses elsewhere in the engine compartment as well with the relays. One of the relays may also be stuck if it got water in it.