Switch to Target Display Mode without keyboard

Here's my setup: MacBook --> Thunderbolt Display --> iMac 27"

The MacBook is the primary computer I want to use; the iMac is the (tertiary) display.

This all works just fine. The problem is, when I disconnect and then reconnect the MacBook, I have to manually put the iMac in Target Display Mode using the keyboard. This means I need to keep a keyboard attached to the iMac, and it clutters up my desk!

Is there any way to switch the iMac into TDM without using the keyboard? Maybe by logging in remotely?

I found a few similar questions, but... no answers!

Is it possible to have an iMac maintain target display mode even through sleep/screensaver

Target Display Mode: how to automate and persist on closing laptop

Anyone?