I am 75% sure that I have found it. An old game expert suggested looking in old catalogs and I found this page in a 1975 catalog:
It's called Shock Tower, the description under the picture says:
"Race against time as each player tries to stack letters on 3 of the pillars, one at a time, until they reach top of tower and spell out S-H-O-C-K ... all in 60 seconds! If you fail, everything knocks down by means of a shock vibrator in the base and you begin again. High impact plastic tower"
Here is an ebay listing with more pictures
Is this it?