In the same situation many years ago (very impoverished) I bought a
newer secondhand battery for my ancient car and put the old car one
into the boat. With just one 10 watt tricolour nav light (the old
fluorescent type that gave loads of light for low wattage but rotten
colour cutoff) and a similar wattage single cabin fluorescent, plus
oil cabin and anchor lights, a charged old battery usually lasted a
couple of weeks summer cruising. Nights are short, and you don't put
the nav light on till it's genuinely fairly dark. If there's was
nothing around, I admit I turned it off.

Can you push-start your car?

Well, I don't think I could push-start it, but rolling down a slope
would work. Unfortunately there is no slope at the marina.
However, I think I won't risk it. Coming back from a cruise and not
being able to start the car will certainly make my wife mad, so I
would have to buy a new battery for this reason anyway.
I guess I just dislike the idea of the thing sitting in the boat doing
nothing, almost the whole year, but needing recharging and
attention...