> there’s no way to trickle a toilet

If you have a tank toilet you might be able to adjust the floater (bend the rod upwards) so it never quite turns off the supply valve. Failing that, you can just manually prop the flap open with something.

If you have a flushometer, remove the nut over the valve and adjust the screw underneath until the valve never quite shuts off.

Warning: Take careful note of exactly how things were before. A toilet that never stops running can be just as hard on the spirit as a toilet that doesn't work at all.