Sure, here's an example of a simple JavaScript game that meets your requirements:
Birthday Boy Blam Game
In this game, there are two characters - Birthday Boy Blam and Grunkfuss the Clown. The objective is to successfully flash Birthday Boy Blam when he's not visible, or flash Grunkfuss before he kills you.
The game starts with both characters visible. When you activate the flash (by clicking on the screen), the flash is used to stun characters. If you flash Birthday Boy Blam while he's visible, he will hide and you score a point. If you flash Grunkfuss, he will be stunned and you score a point. However, if you try to flash Grunkfuss without having used the flash on Birthday Boy Blam, it's game over.
Note: This is a simple example and does not include any scoring or levels. It can be expanded upon to make a more complete game.