I have a client who has an artwork they purchased several years ago that no longer lights. I suspect it is the transformer (rather than the tubes) that has failed. She told me the transformer was checked by someone (I don't know who, maybe her electrician) and that it "works" and "has electricity moving through it" or some such. I'm skeptical, but have not been out to see it in person and test it for myself. My question is, is there a way to test a transformer to see if it working other than connecting the leads to something (like another tube) that I am not aware of? Because the transformer hasn't been disconnected from the tubes, so I don't know how this person would have tested it. But before I tell her she's wrong, I want to check to make sure that I'm not missing something. I've included a photo of the transformer in question. It is a DC transformer and also very small, but it is only running about 2ft of neon.

It is a simple matter to verify that the transformer is getting input power, and that may be what the person did.  However, this alone does nothing to tell you if it is working or not.  Many a transformer, both traditional and electronic ones, have had failures in the secondary side.

To determine if it is bad, there are some options, depending upon what tools they have:

They could simply substitute a known-good tube.  Or, they could use a tube tester to see if the existing tube is good.  Beyond that, to properly directly test the transformer itself, they would need to have a milliamp meter that has a high frequency response to be able to measure the short circuit current from an electronic transformer.  (and this assumes that it does not have a short circuit shutoff protection)  To do this, I would first verify input power of the correct voltage on the input leads using a voltmeter.  Next, I would disconnect the tube and then connect a milliamp meter that is capable of measuring current at a high frequency--a normal mA meter will NOT work on an electronic transformer because they lack the frequency response to measure power on the order of many kHz such as these output.  If the transformer does not have open circuit or short circuit protections, then you can put the mA meter across the secondary and measure its short circuit current just like we used to do with the older style transformers.  If it is not producing the nameplate rated current, then it is likely bad.  Additionally, it is possible that it still produces current but at a degraded voltage that can't light a tube.  The latter failure mode, while possible, is less likely.

Also, in my experience, it is rare to find a customer or an electrician who has the specific tools and knowledge to make these tests with much certainty and so your best bet will be to get the piece in your shop and give it a thorough going over.