Remotely (long-distance) triggering a 12V solenoid?
Ok, so you're drawing no more than 1.7A@12VDC while "active" (solenoid on), and ~128mA while in 'standby.'

If you used this 7.0Ah 12V lead-acid battery (fits in one hand &amp; weighs about 2-3lbs, iirc), that would give you ~4hrs of 'hold time' with the solenoid constantly active, or ~54hrs of 'standby' time.

You could also use larger/multiple lead-acid batteries (heavier, but longer-running), or use Li-Ion/LiPO battery packs (light &amp; high-energy, but costlier) to change the balance of size/weight/power/cost to better suit your specific design budget/goals.