First you have to make everything persist on override so that whatever you override returns when your strobe is over.
Option 1) Open your scene, go to options, in the scene tab under properties there's an Action at end of scene section. Use the drop down to select Add release end cue. Then under timing change the Release Time to 0s and the Asser Time to 0s. From there go to your scene directory and change it to sheets view so you can change the fade time to 0. The result will be a scene that when you click it the scene starts immediately (your strobe starts) and then when you click it again the scene ends immediately (your strobe stops).
Option 2) Move your desired scene to the commands directory (hold open and select commands from the toolbar at the bottom) this will put them on your function keys, next to the command line click on the word KIND (between the M and the ADD) and it will change to CDM. From there you open the function keys (Hold Open and slect Function Keys from the bottom toolbar) you should see your scene on the function key. Go back to the commands directory and put it in sheets view, under the Action header double click and select Flash. Now go back to your scene options and under the Standard tab for the flash key enable + Go on flash and + Release on off. Also go into the Scene tab and change the Release time to 0 as well as the assert time. You will also want to go into your scene directory, change it to sheets view, and change the fade time to 0. This should make it so that when you hold down on the function key your scene is on it triggers and when you release it the strobe stops.