Just for illustration, below is a link to an animated simulation along the lines of what you want to do.
It's to show you were on the right track.
However this is a simplified method, and may not necessarily work in your unit.
The link opens the falstad.com website. Click Allow when asked to permit the connection. Press the switch to see the R1 oscilloscope volt level rise gradually to almost 5 V.
The timescale is expanded. In real life you would choose the capacitor value to produce your desired time delay.
When you release the switch, both L1 and R1 fall quickly to under 1/2 volt.
https://tinyurl.com/d4ustfa
The concept will need to be refined.
It's a question whether it's better to bridge momentarily across L1 and R1. This would involve transistors.
My method delivers a high or low pulse to an unknown terminal. Again, it may not work in your unit.
You want the added circuit to show a high impedance after it executes its purpose. It is not allowed to interfere with subsequent pushes of L1 and R1.