Found a Zenith 5" from 1981

[Jeffhs]

That set looks like a very late-model original Zenith TV, before the company ceased television production in the US (I believe this model first appeared on the market some time in the late 1970s). However, this is the first of these sets I've seen with an LCD digital clock -- the first versions didn't have one.

You are fortunate that remaining battery didn't do more damage than it did. Electrolyte from flashlight batteries (even penlight or AAA cells) is extremely corrosive and could have eaten away one of the terminals of the battery holder, or worse.