This is a 6500K Octron 13 watt 18 inches. Wonder what the CORRECT ballast would be to run this on ? I am using this in my manual preheat desk lamp. I am sure it is some over driven, but the aging looks normal, and it sure is bright !!!!
Also I have a HF ballast that will run F17 through at least F32 T8 lamps. Will a F20T12 run on it acceptably? I may have to make a test fixture if I can't find out......... 
Try following:
1) Connect one of the filaments to 3.5V voltage source and measure the current Ifil.
2) Multiply this by two and you hen a raw approximate of the designed lamp current Iraw = 2*Ifil
3) Estimate the arc voltage: Vraw = 13W/Iraw/0.9
4) Find a ballast capable to feed the desired ballast voltage with a current between Iraw and Ifil.
- If the estimated arc voltage would be below 60V, F15T8 series choke ballast would be good, in series with the lamp and in a "manual preheat" circuit.
- If the voltage would be between 50..90V, use a combination of F4..8T5 choke plus 2.7uF/250VAC capacitor in series, all in series with the lamp and in a "manual preheat" circuit
- If the voltage is 80V or above, use F13T5 ballast, connect as "manual preheat"
This should light the lamp after few "preheat" trials. If the lamp electrodes glow, but the lamp only flash when opening the "starter" switch, go to "one step higher voltage" setup and retry.
5) Start the lamp in one of the previous circuit and measure the arc voltage Vnom by a "true-rms" AC V-meter.
6) Calculate the nominal lamp current as Inom = 13W/Vnom/0.9
7) Find a ballast feeding the nominal lamp current (you may use one of the previous circuits, if it feed the correct current, but check with an A-meter). The ballast current may be in the range of 60..110% of the lamp nominal current.