I'd just plug in the charger and leave it plugged in (to the battery) permanently, unless you intend to leave the HT unattended for several days, in which case I'd disconnect it, then reconnect it for use again.
The battery (assuming it's good), with a float charge on it from the wall wart charger, will power the 2600 forever for packet/APRS work, since the nature of those modes is very intermittant, low duty-cycle with brief transmit periods. I ran a 2600 for years this way as my "main packet station," and although the battery did eventually die, it took about four years for that to occur, and I'm not sure they ever last longer than that!
73 de Steve WB2WIK/6