Sorry, had company, could not elaborate.
Those glow type fuses have a bulb or LED across the fuse link. As long as the fuse is good, its a dead short and the bulb never sees any current.
When the fuse blows, if there is still a load on the circuit, the current flows through the light and makes it light up.
Therefore there is a small amount of current that flows even though the fuse is blown.
If there is no load on the circuit, then the fuse does not glow since there is no current flow.
This is the downside of those type fuses. If you are testing for a dead circuit with a meter, you will get full voltage even though there is not enough current through the bulb to actually run anything.
If the radio is lighting up and then going dead, then something is kicking in. The display on those radios draw a very small amount of current. It sounds like there is enough current leaking through the bulb to run the display.
Then, the full radio kicks in, and the bulb lights. But there is not enough current to actually run the radio, so the voltage drops below what it can run, so it shuts down.
After the shutdown, it goes through the start-up procedure again.
Now, the question is, what keeps blowing the fuse?
Couple of possibilities.
The most obvious is a short between the fuse and the radio, probably caused by a pinched wire from the jolt of hitting the mud hole.
Easily checked, just disconnect the power wire at the radio and try a new fuse. If it blows, then you have your answer.
I can give some tips to find it.
But, if it does not blow, but does when the radio is hooked up, then there is another possibility.
It depends on the type of output circuit in the radio. But, a shorted speaker wire can cause the fuse to blow when the radio turns on the speaker.
Since radios are computer controlled these days, there is a basic startup procedure. The computer turns on, goes through a check out routine, then turns on the speaker amp.
That may be when it blows, and also why there is a delay for the fuse to glow.
I would also use regular fuses while testing to eliminate another variable.
