Replaced dash - guages drop, turn signal relay buzzes

[cougarmt]

My son and I just replaced the entire dash in his '87 325e (yes, we're still questioning our sanity...!), and now we have two residual challenges (so far...) -

First challenge: After reconnecting the instrument cluster, all guages come to life after starting the vehicle. However...after about 2-3 seconds, they all drop dead.
After reading a BBS thread about similar behavior, we went ahead and replaced the (2) 3.0v batteries on the instrument cluster circuit board. Same thing happens after starting the vehicle; guages come to life, guages drop dead.

Second challeng: The turn signal relay switch emits an annoying midrange buzzing sound when placed in either the left or right signal position, and no light activity. We swapped out the relay switch with a brand new one, but get the same buzzing sound, and no light activity.

I'm thinking the turn signal issue may be related to a loose ground wire (although the connector at the switch-to-steering column is in place).

Any thoughts, suggestions, advice would be greatly appreciated, as we're trying to have it back on the road for his first day back at school (in a couple days).

Thanks!