This sounds like a dash dimmer (your headlight switch control) problem.
Ma did a little "trick" on instrument lamps
First it's important to understand that there are basically THREE separate circuits in the headlight "switch" which is in reality SEVERAL switches -- and the dash dimmer-- in one unit
ONLY the headlights are suppplied UNfused power from the "in harness splice" which goes to a breaker built into the light switch. ONLY headlights
The park/ tail circuit is supplied by a fuse This runs the park and tail lights AND supplies power for the dash light circuit
The dash lights have a separate little fuse (in the box) that is wired AFTER (downstream) from the dash dimmer control
So your circuit path is -- tail light fuse -- light switch -- dash lamp dimmer control -- instrument fuse -- to all the dimmed dash lights
FIRST thing to do is find the INST fuse which I believe is SHORTER than the rest
Below is a screenshot out of the 72 manual. I don't have a 76 manual so this may be different. You can see the light switch and the fuse panel
Here, by the way, are useable diagrams from MyMopar
http://www.mymopar.com/downloads/1976/76ValiantA.jpg
http://www.mymopar.com/downloads/1976/76ValiantB.jpg
came from here;
http://www.mymopar.com/index.php?pid=31
The three fuses on the left are all "ACC" fuses, that is are on ONLY with the key in "run" or "acc"
The two fuses D and E are full time hot and you can see at the bottom that wire L8-14P goes off to the light switch. This feeds power to the light switch for park, tail AND the dash dimmer (instrument) control.
The LAST fuse, F, to the right, is the "trick fuse." You can see at the bottom right corner of the headlight switch, terminal "INST" feeds this fuse. THIS IS the output of the dash/ instrument dimmer control, which THEN goes to this fuse AND THEN feeds all the dimmed dash lights.
Other problems in this area include corroded lamp sockets in the dash, corroded PC board, poor ground at the cluster, and poor connections/ or broken / loose connector pins at the PC board