Turn Signal Indicator On w/Brakes

We have a 2001 Venture and I noticed that when I hit the brakes the turn signal indicator lights on the dash were lighting dimly. If I use the turn signal it stops doing it.

I was thinking maybe a bulb filament was shorting out, but my turn signals and brakes do not share a bulb.

Any ideas where to look? I'm pretty sure something is shorting out somewhere.

When this happened to my 02 over a year ago, I changed the bulbs and that didn't help. Usually it's the bulbs.
I found out that the wires to the plug on the rear light was showing burn marks and the contacts were corroded with white stuff like hard water. Anyway, if the new bulbs don't do it, check the wires and plugs and make sure they're all ok.

Hope this helps.