Hi, my front right tyre keeps losing pressure.

Tyre shop have done a water test and pressure test but can't find the leak. They didn't take the tyre off the rim and feel for a small nail (I'll do that next). The valve core has been swapped, but I keep getting low pressure after a couple of days.

Have only done 40,000 KM so too soon to replace all the tyres and I don't want to replace just one (uneven wear).

It has been suggested to me that I have the tyre shop insert a tube. Can anyone advise if that would interfere with the tyre pressure gauge on the dashboard?

Any other suggestions?

Many thanks.