A suggesting to be taken with caution.

I am not sure if what I am suggesting is right or will help, but I wonder if giving him a formula for baby squirrels might help him. I think (but not sure) that even an older squirrel if injured may take milk after they are weened. I believe that milk may not have as much calcium as something but still it is a good source of calcium because it is absorbed well. A formula that is more natural than what is often recommended is: 150 ml goats milk, 50 ml yogurt (a store near me has sheep’s milk younger) 50 ml heavy whipping cream, The contents of one capsule of probiotic with a lot of different strands. (Renew Life’s Ultimate Flora has 40 Probiotic strands (150 Billion Live culture per capsule). If you add honey he may like it better about ¼ teaspoon. Mix the honey in a part of the milk, warm and stir the honey in then add this to the rest of the milk. You may also want to add some coconut oil when mixing in the honey but it tend to clump when it cool. The main ingredient of this formula is 3 parts goats milk, 1 part yogurt and 1 part heavy whipping cream
I am not an expert and I am not sure if this is good advice , but if he likes this I do not think It can hurt him. If you do not know if he is getting too much Calcium or too little I think because this is a more natural formula either way it will be good as far as calcium is concerned. I like the taste of this formula myself, but I do not like the taste of reconstituted milk. I think because of the yogurt in this formula it will keep longer than most formulas. When it gets older it becomes more like yogurt but does not go bad fast. Goat’s milk is said to be digested easier than cow’s milk
If he does not like to have thing syringed to him maybe he will drink it out of a bowl.