<...continue with the work when the test equipment reads zero...>
A correct procedure would be:
Lock-off the circuit being worked on.
Test that the test equipment is working.
Test that the locked-off circuit is dead, using the tested test equipment.
Test that the test equipment is still working, by re-testing it on a live circuit.
Issue Permit-to-work to the individual leading the work on the dead circuit, preferably handing the individual the key to the lock so that it can be returned when the permit is either cancelled or completed.
__________________
"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856