I'm not a professional calibrator, but I'll put my 2c in since this is a subject that interests me as well.
As others have already mentioned, the white clip, needle pulse, and blooming tests are not really designed to achieve the optimum white levels for viewing. They are designed merely to test the display's limits in this area. The optimum setting for white level depends primarily on 3 things:
1. The ambient/background light levels in the room.
2. The display's gamma.
3. The brightness of the content being displayed.
This is why eyeballing really is the best method. And simply assigning an arbitrary value such as 30 or 40 fL may or may not deliver the results you want.
If you don't trust your eyes to make the call unassisted, then the next best thing is probably an ambient light reference. This will take into account the first 2 items (room lighting & display gamma), but some adjustment will probably still be necessary to compensate for the different brightness of content being displayed.
Several of the calibration discs include some type of ambient light reference in their video setup patterns. The SD Component video edition of DVE for example includes one at Title 12/Chapter 16. The idea is to insure that the room lighting does not excede the brightness of the gray swatch in this pattern. It does not really give a specific target for optimum
room lighting though.
I'm not really sure what the industry standard is for ambient/background room light. All I've read is that SMPTE recommends no brighter than 10% of the display's peak white level (probably measured from a 100% white window). I'm guessing that this "10%" value is in cd/m^2 or nits, because the max. ambient light pattern on the SD edition of DVE is actually about a 35% gray. In my own tests, I found the best level for background lighting for my display (34" CRT) is probably about half that, or roughly the equivalent of a 15% to 20% gray on the screen. (YMMV of course.)
Instead of adjusting the room light though, you can simply tweak the white level
on the display until a flat field gray pattern in that brightness range closely matches the background lighting in your viewing area. And that should put you pretty close to the ballpark for comfortable viewing, with no light meter required.
There will probably be some variation from display to display, so if the picture is still too bright and fatiguing to the eyes with a 15%-20% ambient/background reference, then try adjusting the white level with a slightly brighter
ambient gray reference more in the 20%-25% range. Or if you're having trouble making out shadow detail (with gamma and black level set correctly on the display), then you might possibly want to try adusting the white level with a slightly darker ambient gray reference. I would not go too far below a 15% gray though because the peak whites on the display may begin to appear quite bright (unless the display has some type of contrast limiter
that automatically clamps down on high APL images).
You also want to try to stay within the white level limits defined by the other test patterns. If, for example, the ambient light reference calls for a higher white level setting than the other peak white level tests recommend, then you may need to reduce your ambient/background room lighting a bit to help bring the peak whites down to a level that's more manageable for your display. This might occur with some direct-view CRTs.
With LCDs you could run into the opposite problem, and might need a little more
ambient/background light to get more contrast out of the display, and some more depth in the blacks. Plasma displays could go either way, depending on how good the blacks and contrast are on a given model.
Anyway that's my layperson's suggestion for folks still having some difficulty finding an appopriate white level for their direct-view displays, with no special equipment needed. Hopefully some of it makes sense.