Driving compact UV lamp with DC
Ignition voltage is unknown yet, may be 68V or 2x conduction voltage , so 1:6 transformer with current sensing regulating seems feasible.  Unless centre tap doubles this ratio with Vpp ratio

It seems your 2 pin tube is designed for magnetic ballasts with internal switch while 4 pin versions are for electronic ballasts.

Here is a magnetic entire solution for &lt;20$. https://m.ebay.ca/itm/UV-disinfection-lamp-electronic-ballast-PL-S-5W-9W-11W-universal-lamp-holder/182962632880?hash=item2a996c38b0%3Ag%3A6LsAAOSw0RdaMgVr&amp;_mwBanner=1&amp;_nkw=pl-s+ballast&amp;rt=nc

But it’s not dimmable.