Help requested for electronically controlled switch.

Hi.  First off, I am not an electrical engineer.  I barely can solder.  I think this project is extremely simple and I have brainstormed several possibilities to make it work.  I figured I’d post here for input from people that may know what they’re doing and could offer me some advice.  So I have an Icom 7300 Ham radio.  it has an accessory port on the back with switched 13.8v  signal [1amp max] and of course a ground.  I also have a Palstar HF auto antenna tuner.  What I am trying to accomplish is when the radio is on, the HF auto turns on, and when the radio switches off, the HF Auto switches off.  Both pieces of equipment run off of 13.8v DC and are currently using the same power supply.  So I’ve decided the most simple circuit is to use a mosfet capable of handling 3.3amps which is what the HF Auto needs and switching  the mosfet with the radio 13.8v.  The Gate will be connected to the switched 13.8v signal from the radio. The source and drain pins of the mosfet will switch on and off the ground or negative lead from the power supply connecting to the HF auto.  The positive power for the HF auto will be left uninterrupted from the power supply .   I understand that the gate needs to have a draw down resister as well as a resister to limit inrush current.  I’ve decided a 1k for the inrush protection and a 10k for the draw down resister.  I might add that within this circuit, the grounds are going to be separated; the radio side from the switch power side.  I think this is best to prevent a ground loop within the circuit as the actual power supply still be delivering power to both the radio and the circuit, even with the radio is off.  I’m sure that all this is confusing and I’m missing something so please ask questions, affirm my design or tell me it’s crap and offer an alternative.  I decided to go the mosfet route to avoid relays and the need for additional diodes etc.  I’m not completely settled on this design so please chime in.