The relay is supposed to turn on when the ECU tells it to and not cycle off until it tells it to. The problem is that if the relay is failing or the connector has been repeatedly overheated, at temp (temperature of the relay), it can fail to have enough oompf to close the contacts even with the signal from the ECU.

The main pump and in tank pump are controlled at the same time by the relay.

Since this is an intermittent and rare failure, there is no way to guarantee that the main pump is not bad, but it low on the list of likely failure items.

Since it looks like you are back home, do the thermal paste on the power stage either way.