If I’m the traffic that is on base, I get very chatty in such situations, there’s no rules saying you can’t add your own extra positional reports and it helps everyone’s awareness.
Something I picked up flying at DX which can be very busy with vastly different aircraft types (where else can you find a Tiger Moth, Spitfire and PA28 sharing a circuit) everybody kind of communicates positions by telling the FISO, remember everyone can hear when you tell the tower.
If the tower is shut, my calls to “traffic” will be more often than usual on my approach to the field.