"I would first assume"
Assume nothing unless you have money to burn. Did genuine battery shops disappear off the face of the earth when I wasn't looking?
Mark the wires according to the terminals. Remove the battery and take it to a rootin' tootin' battery shop and they will charge it, hydrometer test it and load test it. If the battery needs to be equalized they will do that too.
Batteries need to vacation fully charged. Trying to charge with a trickle charger would be like fighting a kitchen fire with a squirt gun. A discharged battery DOES NOT HAVE THE LUXURY OF WEEKS to recharge. Hard sulfation will form between start and finish and you will gave doomed he battery.
If a trickle charger is all you have apart from the pseudo charger in the rig, you need some way to fully charge the battery. Easily. Fully. No guesswork. Many on this forum have a primary charger to raise voltage to a reasonable level then a mechanical charger to take over when the smart charger goes stupid in order to finish the job.