Well... Yeah...
While using the "Camp Clothes" sheathed weapons aren't shown at all. So the Light enchanted weapon is not there to produce the light. (Same as if you enchanted a melee weapon and then swapped to your ranged weapon. As the melee weapon is no longer being shown, it's not producing light)
Pressing "U" to unsheathe weapons works to get around this (The caveat being entering dialogue causes forced sheathing so you'd have to unsheathe them afterwards)
Of course, Wildshaped Druids are screwed no matter what as they cannot have a weapon equipped while shaped.
Personally, my big gripe with the Light cantrip is it only being Until Long Rest on WEAPONS. If you go through the extra effort of using it on say, armour (Which requires you to remove the armour, drop it on the ground and then cast Light on it and then pick up the armour and re-equip it) it only lasts 20 Turns. Makes it quite annoying for any unarmed characters or characters that weapon swap frequently (Or anyone who wanted the drip of being clad in bright shining armour/clothing).
On a side note:
I hope future Larian games come with a proper transmog feature. So we don't have to awkwardly work around it with camp clothes (Which not only potentially ruins actual camp scenes, but also has aforementioned "Not showing sheathed weapons" thing - To say nothing about not allowing weapons to be visually changed). Also, if they do double weapon loadouts, I hope they properly show both weapon loadouts at all times (Ideally with proper sheathes and other assorted attachment systems)
