Personally I try to limit it to three per cluster with clusters maybe 6"-8" apart. I don't use lights, but that worked well for me in late fall light.
Probably depends on the variety and how large you want them to be. more tomatoes = smaller tomatoes. fewer = larger.

What kind of tomatoes? I have 2 Oregon Spring Bush that are about 40 days old and at about the same stage of development as yours. I have them in drip buckets. Mine have been under a 400 watt HPS light. Grizzman, do you pinch or cut off the flowers to limit production?

yes I generally cut the excess flowers off.
Last crop I got 100% fruit set and waited a few days then cut the stragglers.

yes I generally cut the excess flowers off.
Last crop I got 100% fruit set and waited a few days then cut the stragglers.

Nice, gnomico! I planted the seed in rockwool on December 24, so it's significantly older than yours. 70ish days old. It is the 'early girl' variety, and says on the package '56 days'. Not sure what that meant, but it didn't mean I'd get a tomato in 56 days, I'm guessing.

I planned to take Griz's advice, but the plant did it for me! The spurs have dropped buds to such an extent that only 2 or 3 set, as Grizzman suggested. I'm up to 7 baby tomatoes, and will pick off all new buds when it gets up to 12, just so they'll be (hopefully) full-sized.

I'm bad at taking good advice. I started the Oregon Spring Bush as I thought they would stay compact and allow me to grow other vegetables, such as dwarf peas, cucumbers, spinach, and jalapeños. The tomato plants are getting large, branching out horizontally. Two weeks ago I began monitoring the PPM (and PH) on a daily basis. The plants are "eating" at least 20 ml of nutrient solution per day.

Tomatoes are greedy suckers. Not only is a large tomato plant capable of taking alot of nutrient but in Hot weather, they can transpire a gallon of water per day.

Don't be too fooled by the notion that hydro plants don't need space. Though they can be provided with their nutrient/water needs in a small space, plants like tomatoes will still take up a fair amount of space for their roots and tops. Aggressive training/pruning is needed to keep them from swamping the other plants.

Here is a link that might be useful: My Hydro page