On the TS1610 there are three on positions for the key "on electrical power on", "on with lights on high beam" and "on with lights on low beam". So you should be able to operate the tractor with the key on and the lights off. I think it will charge with the key in the off position, but the operator manual says not to do that. The operator manual does not say why this shouldn't be done, but I think it is because with the key in the off position the warning lights for water temperature, oil pressure and alternator may not work.
Electrical power on with the lights off should be the first position of the key next to off.