It said that if the battery needs charging to place the loco on the powered track for 16 hours. Who in their right mind would do this? Did I misunderstand the instructions or did it tell me to leave thousands of dollars worth of electronics powered up to charge one battery? I wouldn’t do that for 16 minutes. Let alone 16 hours. The seller said he put a new MTH battery it the model before I purchased it. How long can I expect it to last? Have these issues been resolved with new models or is this just the way things are done at MTH?
Based upon the catalog number, (MT5501LP) that is a very old engine. MT ("Mike's Trains") predates Premier or RailKing designations. It is likely from the late 90's.
They do have built-in battery chargers. So yes, you do power them up and let them sit. Batteries are good for at least 3 years. Part of the life depends upon how often you run the engine. The buyer said he put a new battery in it. Simple. Check it with a voltmeter. If it's dead, replace it before attempting to power up the engine. Otherwise, you may be introduced to the "Three Clanks of Death". Do a search here, it has been discussed ad-nauseum.
MTH has progressed a long long way since the engine you have. FWIW, it's probably a great puller.