That Brooks ad wasn't the one I was referring to but I went through the 1983 and '84 Yearbooks and all of the programs from those years again. I found an ad in the 1984 Program with Cal on the front cover that answered my question but it wasn't the original one I had seen (which was an entire back cover ad). Apparently, the cards you received for testing driving a Dodge were 1984 Topps Orioles cards. It's a shame, I was really hoping that there was some obscure Dodge Orioles issue out there to hunt down.
1984 O's Program with Cal.jpg
1984 O's Program ad.jpg