There is, but current-measuring meters are easily damaged because the whole current
flows through them. You can put an ordinary ammeter in series with the battery cable
but if you hit the starter while it is there you'll burn it up.
The beauty of the light bulb tester is that it is sensitive to fairly small current levels
but is not overpowered by the full 12 volts because of its inherent resistance.
An ammeter has little or no resistance.
If you can verify (like with the light bulb tester) that the current flow is small,
you can then more or less safely put an ammeter or multitester set for current in the circuit.
I have not done this yet, considering the time involved. It was pretty quick to check
all the fuse sockets with the light bulb tester. More time consuming to actually
measure small currents (if any).

Voltmeters are high-resistance devices and do not ever get much current.
Ammeters are essentially zero-resistance devices because you have to conduct
all the current to measure it.
--
George Downs Bartlesville, Oklahoma