How to connect a device to ground using negative signal with high impedance
simulate this circuit &ndash; Schematic created using CircuitLab

The "your controller" box on the left represents your "device that enables a ground connection when I press a key on a remote control", I drew a switch with 1k in series, but what is inside the black box doesn't matter.

When the switch closes, it will pull down the gate of the P-channel MOSFET, which will conduct. When the switch opens, R2 will pull the gate up, and the P-MOS will no longer conduct.

This switches the load in the positive supply wire, which may be more convenient than switching the ground, especially if the device that is switched must communicate with other devices, in this case it needs GND as a reference for signals.

Since the supply is 12V, it is not necessary to protect the PMOS gate (most will tolerate up to 20V).

Voltage drop on the PMOS will be RdsON * current, to minimize it try to pick a PMOS with a RdsON below 0.1R at Vgs=10V, that's easy to find.

You can also use a PNP transistor instead of the PMOS, same schematic but it will need a base resistor, which depends on the transistor's gain. For 150mA it's better not to use a 200mA transistor, so if you have some PNP transistors already which can handle 0.5A or more, post a link to datasheet if you need help picking the base resistor.