Hi, new to the board but not to Trek. I'm also interested in what the 4 glowing things are. Having read the relevant parts of the thread my take is that TOS was pretty poor in terms of continuity and design. I prefer to consider the later works as building on that canon which means that whatever those things are they have to have some kind of relevant evolution in later incarnations of starship. The most obvious conclusion is that they serve the same function as the lighted areas on the refit. The top and bottom have openings directly beneath the bridge and on top of the lower sensor dome which are lit. In semi-canon literature is usually identified as the sensor array. So these could well serve the same purpose, especially as a subspace array where the concept of direction is irrelevant in that the sensor is digging into a completely separate domain which doesn't follow the same dimensional rules as this level of the universe. Making them sensors makes a lot of sense having the additional planetary sensor dome at the bottom being lit in the same way. Perhaps sensors need to be lit for some reason, either the light is a shield of some kind to deflect harmful radiation or particles or sensors in TOS period simply give off light as waste energy. Talking of energy, they could also be part of the shield system or even something to do with the transporters considering that no other external detail deals with this function when everything in TNG did have some kind of detail to represent this important system.
I like to think of them as sensors because it's the only thing that makes enough sense. The dome under the saucer and the four squares lit (I believe they were meant to be lit, just like there was meant to be a grid which was only penciled on) strongly indicate that they function as some kind of sensor network. I also like they idea of them serving as a high energy transmitter, perhaps part of the shield working in tandem with the domes which also nicely explains why the weapons are fired so close from the dome. You already have a high energy power source there and it would be easier to fire energy through directly along the plane of the shield transmitter. The only argument against this is that there is nohigher energy system than the deflector and engines and they don't glow at all (although they were intended to but couldn't due to budgetary restraints. To deal with this to a degree, in TMP they only glowed when functioning at warp as a kind of suggestion that they were glowing on the older version but we just never saw it.) So that kind of upsets the theory of a shield network because they're always glowing and high energy systems aren't glowing at all. The only thing in TOS that always glow is the sensor dome so that's where my vote goes.