By the way, any chance you have a "loose" diode or even a bridge rectifier (as shown in previous post) sitting in a junk box or whatever?
There is a even-odds chance that a single 5-cent diode could solve your problem...not that you can buy just 1 diode!
Anyway, inserting 1 diode in the wire to the lamp will cut the voltage roughly in half - it's not exactly 1/2 (again, the math is tedious). The single diode is converting the 16V AC to a pulsed DC that just might work. This technique was commonly used in rolling stock to dim bright incandescent bulbs when the conversion was made from conventional to command where 18V AC was now on the track overdriving the (typically) 14V bulbs used in passenger cars, cabooses, etc..
