Checked the resistance (my Fluke calibrates zero with the resistance of the leads) and get c. 0.1 ohm or less for the bit. Secondary winding resistance is below my meter's resolution, 6 turns of c 8 gauge wire, so no surprise there.

The bulb winding is deffo not in series with the primary, measures 1.5 ohms. The primary measures 86.5 ohms, live to neutral no bulb in holder. Interesting the difference in inductive load, because obv if that was resistive, it would be running at (takes off socks for counting).....700ish Watts? Nominal load rating is 100W.