Galaxy Electronics Corp. - Galaxy Game 2001 (1980, LED, 9 Volt, Model# 3001)
One or two players can play one of 3 different games: Cross Fire, Pass Thru and Follow Me. This game is made by a company called Galaxy Electronics Corp. which was based in Taipei, Taiwan. It's also part of the '2001 Galaxy Series' of games and toys. The series consists mostly of toy ray guns and targets, as well as this handheld game. (I have a slightly different version of this game listed as Space Invaders, I'm pretty sure it's one of theirs.)
Ad from Playthings toy trade magazine:
Do I have this? No (but I have the box...).