Sounds like the drip is coming from the HVAC (Heat Ventilation Air Condition) cabinet. Grate on the bottom is probably the outside air intake. Both Heater Core and A/C Evaporator (cooling core) should be in there. Maybe a Water Control Valve and that could be leaking, but recent HVAC doesn't use a Valve. Instead it uses a Blend Door. Both Heat and A/C are producing full Hot and Cold; you set the temp you feel by positioning the blend door.
Neighbor had a 40' Winnebago DP with a leak up there. I bypassed the core with a length of heater hose till he had it fixed. I don't know what was involved inside.