One kind of centre finder on the market has a slot for a pencil to mark intersecting diagonals. These work well on squared timber, but are a bit slow to use on a batch of items. Another kind has a blade. You position the blank, tap it so the blade makes a diagonal line, then repeat. I’ve found that this type can easily start splits in the wood, and needs the end of the blank cut square.
The centre finder I used for a long time is simply a small wooden block. The block has a hole drilled that is a push fit for a short pencil. The hole is off centre. By turning the block on different sides there is some height adjustment. To use it, I put the spindle blank and the pencil block on a flat surface and mark a line across the end of the blank. Then I flip the blank 90 degrees and repeat to do all four sides. The result is a small square marked on the end of the blank, from which I can easily find the centre by eye. This is not super-accurate, but good enough for most purposes, and it is quick. I have several blocks in different sizes so I can pick the one most suited to the size of the spindle blank. The blank need not be square and the pencil block can mark cylinders equally well. The point of a nail works too, and stays sharp.
I’ve now made an adjustable version of the pencil block, with a pivoting arm to hold the pencil. The hole for the pencil has a slot through it and a pinch bolt to lock it.
To find the centre of a bowl blank, I usually use a hardboard disc of appropriate size. I have a lot of these in different sizes for marking out bowl blanks, and each has a small hole in the middle. I just lay one on the blank, and place it quite accurately by eye or touch. Then I mark the centre with a pencil through the hole.
When I need more accuracy, I use a chuck insert centre finder. This is a short dowel with a steel point in one end. I turned the insert to fit inside the body of my engineering chuck. I put the chuck on the bench and adjust the jaws to be a sliding fit on the spindle blanks. The blanks must be square or cylindrical. A tap on the end of the blank pushes it onto the point to mark the centre. This is a good method to use when part of the finished item needs to be left square.