Is that window cold or drafty?
The purple tubes may be filled with mercury vapor (with phosphor coating to generate purple). If that’s the case and the area in front of the window is colder than the area in front of the wall, then the Hg in that tube may be taking longer to fully evaporate and thus is staying dimmer longer.
Also, if any Hg got splashed on the electrodes (during shipping for example), it can also take a little longer to fully vaporize.
I’d test it by moving to an area with more stable temp. before deciding the tube is bad (which is a possibility too).
(Great sign, I bet those colors look phenomenal together in person.)