I think your tree wants to be outside more. Can it be taken outside for the warmer months. At ten years it should be producing even from seeds. There can be sterile trees from seeds, they will never produce fruit.
Citrus trees hate to be pruned. Your tree looks like branches have been taken off. They will not produce until they have enough canopy to support the fruit and they will not fruit if you keep cutting off the new growth. They like warmth and a lot of sunshine. They also need fertilizer right about now. For such an old tree, it is in a relatively small pot. I have citrus trees in pots, the pots dwarf the trees and I have them in 20 inch pots, anything smaller and they are no longer in the pot.
Your tree is very tall which makes me think it wants more light and you have it in a relatively small pot which should have kept the tree a lot shorter. It is also not the typical shape of a citrus tree which leads me to think you have been trimming off a lot of branches. Otherwise it does look very healthy.
My in ground mandarins are kept at about 8 ft with pruning. They are dwarf rootstock and over 20 years old. I prune mainy for height, I rarely prune the sides unless they get in the way, otherwise I prune off fruit. The citrus in pots range from 1-5 ft. Most of those are grafted. The one in the pot for about 18 years now has a small canopy less than 3 ft in diameter and is about 4-5 ft tall in a 20 inch pot. It does produce fruit, but kaffir limes are grown mainly for their leaves.
Some citrus trees do take longer than others to produce fruit. The kaffir lime took about 4-5 years. Meyer lemon was from a cutting so it fruited within two years, but has since escaped its 7 gallon pot. My key lime tries, but can't seem to be able to hang on to either the leaves or the fruit. Calamondin, is too vigorous.
Happy gardening in Hawaii. Gardens are where people grow.