Tim, what flashing system do you use, and how does it link into your StopClock?
It's very simple. Instead of plugging my enlarger into the enlarger socket on the timer, I plug in a multi gang switchable extension cable (cut down to about 12 inches for tidiness). My enlargers and my distant 'omni flash/fogger' light are all plugged into the multi gang. Each one is switchable so when I hit the foot pedal any combination that is switched to 'on' will come on under the control of the timer.
I use a low wattage night light bulb in a flexible small desk lamp on a shelf at the back of the darkroom. The hood faces the wall/ceiling, thus dimming it further to allow quite long flash or fog times to use whilst burning in impossible areas. (i can move it easily to give a brighter light but then need a new flash strip, so mostly I don't, as i have it adjusted as I like it). This is some 12 feet behind me and the glow is omni directional by the time it gets to the paper. this is incredibly useful for flashing or fogging whilst burning in. I improvised this system almost 20 years ago and haven't improved on it. If you have my 1st printing book you can see an example of burning+fogging on page 83. it's an eye-opener what this can do.
I use also an enlarger adjacent to the one I am printing on for simple quick max-flash exposures through the second channel of the stop clock. This is hugely convenient as again I can switch enlargers on/of and switch channels in a moment.
I find this works so well for me that I have no need for the RH flasher, but I know many people like it and I don't want to give the impression that I have anything against it - I am a declared RH fan. For me though, having a flasher on the enlarger head would be a nuicance as I would have to re-calculate the flash exposure every time I move the head up/down.
Tim