We were just posting about that. The best budwood comes from 3rd flush wood--wood that has 2 flushes past it. When citrus first flushes the wood is very angular, making it difficult to get a good fit when you try to insert the bud. That same wood or part of the stem, gets a little more round but is still somewhat angular after the next flush--this is 2nd flush wood and is usable, but 3rd flush wood is almost perfectly round and fits well on pencil size stock.
As for time to graft, it depends somewhat on the type of graft, I have had much more success with bark grafting when it is hot (mid summer) compared to T-budding. However, T-budding has worked well for me in the spring and late fall when highs are 70 to 80. For T-budding the bark has to be slipping, and that usually means the tree is flushing. I think it is even better to select a limb that is flushing.
If you graft in the fall, you have to wait until spring to force the buds.
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Skeet