I wonder if a 'booster pack' jump starter thingy would work for you? I use one in a remote shed for a tractor and it works....

Booster packs (they go under other names) keep their charge for a very long time and, being portable, you can charge them, when needed, at home.

If you had one with a cigar lighter socket, you could run a trickle charger from it. Trickle chargers use so little power, it would probably keep your battery charged for a month (wild guess of course). Take it home one night and it would be fully charged again.

Obviously you'll need to change your current battery - once they're flat they're either damaged, knackered or, at best, highly unreliable.

And yes, your crazy speedo is highly likely to be going mental for voltage reasons.

+8 4.8