Our idea on witness testing is to firstly look at the test results on the transformer or cable or switchgear that is being tested to see if they are within spec, but also to ensure that the tests that are being performed are being performed correctly, and that the manufacturer has a system in place for eliminating a problem from happening again if something fails. You look to see that they have a system of calibrating their instruments, and that they are fit for the purpose for which they are to be used (ie not using a multimeter on resistance mode to measure the resistance of transformer windings).
Once you are happy with the test methods and that the results are correctly measured, then there really is no technical (as opposed to holiday) reason to be witnessing there again, except for some special circumstance.
To make witnessing worthwhile, you need to send people with test experience who know what tests need to be done, the test methods, and most importantly what can go wrong in measurements that can give false readings. Partial discharge testing is a common one where factories tend to eliminate noise from cranes, lights etc via a gating function. We have seen some manufacturers that have essentially gated out all the actual partial discharge, as well as the noise, so they record it as a pass, when in fact, the test has failed. In essence, to be of value, you must have people who know what to look for, rather than just looking at numbers produced by the manufacturer.
But to answer your original question, if there were time restrictions, then I would be there for dielectric tests (Applied, induced, PD, impulse), then I would rank the heat run next, mainly because the results of it are based on the loss measurements anyhow, but this is a time consuming one - you may want to come in on the end of this one when they are shutting it down and measuring the resistance when it is hot. If they are doing these correctly, you can take a fair bet that the resistance, ratio, impedance, oil tests are going to be done correctly. While you are there, look at the equipment they use for the other tests, see if it is in calibration. Ask the testers how they perform the other tests that you haven't witnessed. By the end of this, you should have a fairly good comfort level as to the correctness of the test methods and results.
ausphil