If your taper is anything other than dead on 8 degrees, you will find that the workpiece can wiggle a little because either the front end or the back end of the collet can move in the holder. Just close isn't good enough. If you have .001" too large at either end your workpiece can be several thousandths out two or three inches away.
Don't be overintimidated by that because if you find it's off a little you can adjust the compound and finally polish a tiny bit out at the end. You've got lots of chances to adjust and re-cut till it's right. However, don't plan on polishing much out because it's easy to get a bellmouthed condition which also won't register properly.
Since you already have ER-40 collets on hand (I presume), you would be able to chuck a piece of stock, turn it to a close fit for one of the collets, put a collet on the mandrel you've just machined and then mount an indicator on the compound to see if it's tracing the collet accurately.
"Opportunity is missed by most people because it is dressed in overalls and looks like work." Thomas Edison