For a normal sleep schedule, you get those LH pulses throughout the early morning which initiate the corresponding secretions of testosterone. The reason you try to get your testosterone as close to 8 am as possible is that that is when testosterone peaks - actually a little before usually - and so you are getting the max read for the day.
Basically shift work modifies all of that in rather unpredictable ways. For example, check out this study:http://www.springerlink.com/content/w4633732864463r3/
And then look at this study where they examined a group of well-adjust men (to shift work) and found a pattern. However, some guys deviated substantially from this pattern:http://ajpregu.physiology.org/content/265/1/R261.short
So it sounds like assuming you are peaking at 8 am is not necessarily a given and perhaps you want to ask your doc if you can get a couple of reads similar to what they often do with cortisol? Because you're not on HRT, right? If you're on testosterone therapy, that's a different story of course.
On the other hand, peak to valley diminishes as we age and you're middle-aged, right? If so, then it may not be worth the cost. You'll have to discuss that with your doc, who hopefully knows something about the subject. There's a little info here as well as far as the peak to trough ratio for different ages:http://www.peaktestosterone.com/Testosterone_Daily