Greetings, I am simulating the following circuit:
I would look along the lines of some real world equivalent.
For example, use 2 2k resistors in parallel and open a switch or MOSfet at your time of interest.
@paulvdh’s answer is definitely the recommended way to do this.
You can also do it with a behavioral resistor, but it’s harder to set up and can cause more convergence problems.