Well thanks to an "assist" from someone who goes by the name "ecloy", I was directed to another player who had a long gap between baseball card appearances, Brock Davis. (Thanks for the heads-up!)
Davis first appeared on a rather famous card, the 1963 "Rookie Stars" card which also happened to be Willie Stargell's rookie card!
On that card Davis was a 19-year-old member of the Houston Colt-.45's, who would go on to appear in 34 games for the Colt's, posting 11 hits in 55 at-bats while fielding all three outfield spots. Take a look:
However the rest of the 1960's would generally be spent toiling in the Minors for both Houston and then the Chicago Cubs affiliates beginning in 1969.
Davis did put up some decent numbers in the Minors, but couldn't seem to break through on the Major League level.
He had one Major League at-bat in 1964, 27 in 1966, and only three in 1970.
However, even with those three at-bats in '70, Topps gave him a spot on high-number card #573, 1971 Chicago Cubs "Rookie Stars", based on his killer Minor League year with Tacoma of the Pacific Coast League.
For Tacoma that year, he hit a robust .332, scoring 77 runs on 166 hits over the course of 500 at-bats. Not bad at all.
But sadly for Davis (and Chicago I'd guess), it didn't translate to any Major League success, as he hit .256 for the Cubs in 1971 with no punch whatsoever.
In December of 1971 he was dealt to the Brewers with pitcher Jim Colborn and Earl Stephenson for Jose Cardenal (remember the late series Topps "Traded" card of Cardenal in 1972?), but even though he managed to hit a nice .318 over 85 games for Milwaukee, that would be the last taste of Major League action he'd see.
Davis would spend another three years in the Minors for the Padres, Cubs, Brewers and Indians before calling it a career after the 1975 season.
Thanks again to "ecloy" for the tip!