A bit of searching on
The CWR▸ Signalling website yields the following:
The railway is one of only a few heritage lines in the country to cross a main road.
The CWR in preservation form pre-dates the road, and as part of the agreement to build the Wallingford By-Pass, it was agreed that Oxfordshire Highways would be responsible for all maintenance of the crossing through Oxfordshire county council (OCC). OCC have a contract with Network Rail for all maintenance of the crossing.
i.e. No maintenance burden for the railway. Good!
So it seems to be another job for the Orange Army. Well they better arrive soon because OCC says on
their roads website that the lights are only there until 18th August. I expect an alteration to that timing soon.