I forget exactly what that does, it's either to help with idle or it's to help with the evap system.
I watched the video, your fuel flow is much too low. It's not zero so it seems like the pumps are working, or at least one of them is, at least a bit. It should pour out, not torrential but a good solid flow, in the vague ballpark of 1 litre every 30 seconds.
You won't have an engine bay fuse on this model year I don't think, I'm pretty sure that was introduced a bit later.
But what you should do is bypass the relay and power the pumps directly from their fuses. That way you can listen to them without the noise of cranking.
If both spring to life and you get good fuel flow then the KJet relay is perhaps the issue.
If you hear nothing at all, both pumps are most likely dead, or you have a wiring issue between the fuse and pump.
If you hear whirring, you can put your ear to the fuel filler neck to see if it's the intank pump or main pump that's operating, and go from there.
One pump failing will generally shorten the life of the other as it will be loaded up.
Also, there is one more fuse you can check, it's in the boot, if you follow the cable sleeve out of the fuel tank access panel, it goes toward the passenger side and under a plastic cover. Remove the cover, under you will find a black plastic cylinder thing, twist to open, fuse inside.
