The ideal situation is to be grafting dormant scions onto recipient plants that are waking from dormancy. There are a few ways to get oneself into that situation. When working at home with hobbyist-level of equipment (i.e. without temperature controlled greenhouses), one way to achieve this is by taking the scions a few weeks before you intend to graft them, storing them in the fridge, and then grafting them later when the recipient-tree is waking from dormancy. This is an especially useful approach if you are taking scions from the same plant onto which you intend to graft. If you are taking scions from a different plant onto which you intend to graft, you may simply be able to keep the scion-plant dormant while waking up the receiving-plant early (e.g. by bringing it indoors--but this could be challenging depending on what your Springs are like).
Several Japanese books on Ume note that scions can be taken up to 1-month in advance. Personally, I have stored scions for 3 months in my fridge prior to grafting without affecting the success rate of the grafts, but the shorter the period the better.
I am starting my response this way to make the point that the moment when you take your scions will almost always be after flowering (I say almost always because I know a few guys in very warm climates who need to take their scions before flowering to ensure that they will be dormant and will remain so in the fridge--this brings another set of considerations that I will ignore here). With the flower buds out of the way, you should be able to visually identify where there are vegetative buds, and where there are no vegetative buds.
Untouched, Ume tend to send new shoots from the branch tips. Therefore, using scions from the branch tips will increase the odds that you will have vegetative buds on the scions. However, branch tips tend to be relatively thin, which decreases your chance of success with the grafts. I would not use branch tips: if you're defoliating throughout the summer (either using POCD as recommended by Bjorn, or using the trick described by Lynn Perry Alstadt but over a greater number of nodes than the recommended 2-3), you should have plenty of vegetative buds along your shoots. I am in the middle of the process now, and some of my shoots as long as 60cm have vegetative buds at almost every node. (If I were trying to ramify, I could cut back to almost anywhere on the shoot and expect shoots to emerge very reliably in Spring).
Here is an image of the majority of books I reference. The second one at the top (NHK, white, red flowers) is by far the most useful book for bonsai. The book on the top right (Bonsai Senka, maroon) is also very very good. (Some of these focus almost exclusively, and very technically on flower types--a taxonomists dream--which may or may not be of interest to you). Send me a PM if you want to any of them and I can provide ISBN and contacts/sources. They can easily be read with Google Translate app's live translation and some patience -- should not be a problem for a fellow academic
@leatherback