more than likely dodgy connection/wiring on your speedo sensor in your diff, mpg gauge works off your speedo so when it stops they both do.

 

I had a problem with the clocks like you do and I subsequently found out that my regulator was gone, the battery was boiling off liquid ,the level became low and every time I took a corner the fluid would slosh over to one side, cut the power and the clocks would shut down, only to come back again when I resumed going in a straight line..
Maybe you should check these

 

Which regulator? It's only the speedo and mpg guages! Where would be the first thing to check

 

Re-read your first post and on second thought, I don't think that is your problem..
I'd check the plugs at the back of the clocks first then check the engine bay wiring to see if there's anything loose or frayed..

 

I'd agree with Kev. Sounds like the speed sensor in the diff is going. Check there first. 2 wires going into the back of it. Nothing in the engine should cause both to go.

My speed and MPG were both off all the time when I had my speed sensor disconnected.