I would check the sockets on your bulbs. I know it sounds "out there", but I had a comanche that did the same thing.... whenever you turned the blinker switch on, the lights on the dash would light up solid, or not come on at all, depending on what type of flasher relay was installed.
After changing the column switch, blinker relay/flasher and generally banging my head over it, it turned out that one of the front sockets for the turn signals was bad... it must have been melted internally so that one of the positive leads was back-feeding the rest of the circuit. I don't recall the exact behavior, but I know I scratched my head for a while figuring it out.
If you haven't looked yet, pull the lenses off and inspect all 4 bulbs/sockets. I'm sure if you thought about it for a bit and looked at a wiring diagram, you could test them, but I went ahead and just replaced the front two with 5 dollar ones from the "help!" section at the parts store that matched the old ones.
