I am not very familiar with probe-start lamps, all I had previously were 2-electrode. In theory, this is not the best to have molten halide pool right across the main and starting electrode. But the web search for lamp data gives inconclusive results, some probe start lamps are listed as universal position. And these are Chinese origin, so unlike Osram or BLV it is hard to find proper  datasheets. What do you think? I suppose tubular lamps are usually expected to run in floodlights in horizontal position, but not 100% sure.

Each lamp model has defined by its manufacturer a range of positions to operate at. You should always follow that.
It is not only verical vs horizontal, but it could be certain exact orientation only, or certain position being excluded.
There are many technixal details at play, some more obvious, but as well many not obvious at all.
Not following them may lead from nothing at all (because such position was never ever considered with that lamp type but it just happened to be fine by sheer coincidence), through some performance degradation, through compromised reliability, to becoming a severe safety hazard.
The problem is, you never know which is the case for your lamp and intended position.

With probe down you may risk it becoming shorted by the condensed mercury or the seals being attacked by the fill still in liquid form when there is a voltage present, but if that position is within the formal burning position rating, it should not be that big of a problem.

If the lamp is rated for Universal burning, it should be relatively safe to run base down, but life might not be as long if it is operated in this position for a prolonged period of time.

but life might not be as long if it is operated in this position for a prolonged period of time.

You may find an effect that may impact lamp life in virtually any position, be it the melted salts pooling where are two seals with voltage across them with probe down, socket cement weakening by heat when base up, upper arctube wall exposed to higher heat when horizontal, etc.
Also some effects may not be shortening the lifetime per se, but leading to a more likely violent EOL.

Unless the given position is not allowed by the lamp rating, you do not know which one is the most limiting one, as each effect will be suppressed to some extend by the exact lamp design.

Operating the lamp in positions not formally allowed means also an unknown (to you) risk, you will never know what was are all the reasons behind.

And by the way I wouldn't even be surprised if even the manufacturer would not know how it will perform. The point is, when (assume a hypothetical example) some standard lamp format is specified for horizontal only, the manufacturer designing a product targeting that standard specs, will make sure it performs well when used horizontally as that particular standard spec mandates. But what would be his motivation to spend high $$$ in evaluating that design for vertical burning (reliability tests are the most expensive ones, as it needs a lot of pieces for long time test), when practically no one will be using it that way? So he simply won't have any data for that particular product vertical burning position...

For standard metal halide probe start lamps if I don't know whether it is universal burn or cap up, I test the lamp cap up.

Most MH lamps here are pulse start, but whatever lamp it is, I always try and follow the manufacturer's instructions. If the burning position isn't marked on the lamp or carton, it's likely universal burn, but don't take that as read; look for a data sheet for the lamp and see what that says. Try emailing or otherwise contacting the manufacturer, assuming they're still in business.

Defaulting to test unknown probe start lamp base up makes sense, but it is the most inconvenient way to mount the lamp, of course. Need to use something like a lab stand, or some prop to hang the socket. For a tubular lamp probably the best guess is horizontal, but who knows what Chinese thought. Lamps look like a cross where American style probe-start burners put into Euro style tubular bulbs.

@Medved: If that was as simple as reading the datasheet (as in case with true BLV) I would not ask. For E40 lamps BLV allows any position. Here the lamps are made by anonymous Chinese OEM and passed many hands in supply. And burner styles for 400W lamps look different to BLV (Ushio), not talking about BLVs are pulse-start only.

Lab stands are awesome for this purpose; we have two, one for the smaller lamps and another when we want to use long lamps like 180W SOX.

But beware that if socket get really hot the plastic coated claw may slip. Especially when running a heavy and powerful lamp. You know what will happen next (.

They sleeves over the jaws are silicone, and they are removable. However we've never had the jaws loosen, although when holding our rare 280W SOI/H lamp, the sleeves did soften a bit 

I've just had a shufti on t'interweb, and found this information on silicone. 
So I think we'll be all right with our lampses 

Yes, silicone does not melt because of cross-linked nature of the polymer. It will start to deteriorate when used at more than about ~200C though, but probably OK in this case. The jaws on mine were lined with cork, which is not as plastic as silicone, and will not have a peace of mind to run a heavy lamp vertically without some extra backup.

After the silicone fingers melted slightly, we wrapped them with Kapton Tape 

Yes, Kapton is a weird high-temp material. I was impressed when a piece of Kapton tape generally kept its shape in the flame *when visibly started to glow red* !