A solid state relay like that would work but it's huge (and kind of expensive). They do make smaller ones. Here is an example:
https://www.mouser.com/ProductDetai...GAEpiMZZMv%2b25x33JEohIyFx2cEByrU8yhwD0zlcsg=
$2.45 ea. Handles 1A load. DIP4 size (very small).
The easiest thing would be to use a NPN transistor as a voltage follower. Pretty much any NPN transistor with enough current rating will work. It will have about a 0.7v drop, but that should not be a problem. A TIP41 is an example. These are dirt cheap and can handle 6A.

My brake light draws about 80mA and hasn't had any issues with contact sticking (yet) but I was concerned about it.
https://www.mouser.com/ProductDetai...GAEpiMZZMv%2b25x33JEohIyFx2cEByrU8yhwD0zlcsg=
$2.45 ea. Handles 1A load. DIP4 size (very small).
The easiest thing would be to use a NPN transistor as a voltage follower. Pretty much any NPN transistor with enough current rating will work. It will have about a 0.7v drop, but that should not be a problem. A TIP41 is an example. These are dirt cheap and can handle 6A.

My brake light draws about 80mA and hasn't had any issues with contact sticking (yet) but I was concerned about it.