Yea, the ICM could be the culprit and there is a test...below is the link to one of LT1 sites I use for my '93 LT1...also the link to the test page from a page of great info. for LT1's shbox:
http://www.ls1tech.com/forums/lt1-lt4-modifications-31/ http://shbox.com/page/index.html
TGO is great for info, but the above two are also good help sites for Q & A on LT specific stuff.
The opti and the ICM tend to be the culprits for this issue...ICM being the cheapest at like $80...the opti being $250 for the cheapest GM one we can find on Ebay. If it ends up being the ICM, you may want to do the spacing mod for it when you replace it. Basically, you space it off the head some so some air is between the ICM/coil plate/bracket and the head...basically keeps it a bit cooler. Which is always better for electronics.