Here is a pic of the 11 footer prior to its 1991 restoration. Note the little red thingy on the lower side of the bridge dome.
There's one on the other side as well. They look like they could be lights but there's no indication they were ever lighted.
I strongly believe these were intended
to be lights and my firm belief stems from the fact that we do have one identical red thingy or "cone" on the upper engineering hull
just ahead of the hangar dome.
Notice that the red translucent cone is surrounded by two circular windows. On the WNM pilot model the center objects of those "triumvirate" windows were lights (saucer bow, saucer underside port and starboard) but for a reason I do not know they decided not to turn the cone on the engineering hull into a light and decided to use the hangar dome instead as a running light.
When they prepped the 11-footer for the regular series they turned the hangar dome into a constant light and placed the running lights port and starboard, the cone remained unlit.
Curiously, TOS-R turned these running lights into ion pods and now turned the cone into a running light.
"In-Universe" I believe these cones to be subspace radio transmitters (looks to make sense to have such transmitters in close vicinity to the bridge, IMHO).
P.S. Note the little miniature train accessory people. If I'm not mistaken their international scale is 1:87 which might suggest the original model to have a scale of 1:96 or smaller if the turbolift extension is a reference for scale.
P.P.S I find the stern windows of the teardrop to be most perplexing. I had thought these to be circular.
May we trouble you to tell us the link where you got this pre-"restoration" shot from?!?