"We suspect that a small amount of an electrohydraulic control (EHC) phosphate ester fluid was added to a reservoir containing a polyalphaolefin (PAO) synthetic. What is the best way to figure out if this has in fact happened?"
For oils that have wildly different base stock chemistry, the simplest method is usually Fourier transform infrared spectroscopy (FTIR). FTIR looks for functional groups in the oil sample. These functional groups act as molecular fingerprints to identify different components in the oil, as well as common contaminants such as water, fuel and glycol.
In the case of phosphate ester contamination of a PAO, you would be looking for a peak in the FTIR spectrum around the 1,700 to 1,800 wave number corresponding to the phosphate functional group. Because this functional group will not be present in the PAO-based oil, any signs of a peak in this region may suggest cross-contamination. By comparing the spectra of a new sample of the PAO-based oil, a new sample of the EHC fluid and the suspected blend, evidence of cross-contamination should be fairly easy to recognize.
Most oil commercial oil analysis laboratories should be able to conduct this test for you.