Get a program that will display *all* of the EXIF data, not just the named fields, such as this.
Open a recent image, and look for a line like this:
Unknown (0093)3,9: 18,Y,XXXXX,0,0,0,65535,65535,0
If Y = 0, then count = XXXXX. But, if Y > 1, then count = ( Y * 65536 ) + XXXXX. (In other words, Y is a “rollover” counter that increments every 65536 shots.)
This is a shutter actuation counter, and it increments even if there is no CF card installed, or when shooting tethered, and is not affected by any type of file number resetting. Removing the backup battery for a full day failed to clear the counter, so it appears to be non-volatile.