The Jaguar XJ-S Repair Operation Manual in Supplement C for 1988 1/2 - cars calls for use of Univis J13 Hydraulic Fluid.
Univis J13 is a petroleum based hydraulic fluid that was made by EXXON, but no longer is available, although EXXON does have other fluids called UNIVIS listed on their website. The site information on the two Univis fluids listed did not indicate if either met Univis J13. It is currently available as a Texaco Aviation Hydraulic Fluid according to a websearch for Univis J13. I went to a local aviation parts supplier Falcon Crest Aviation Supply based in Houston, TX (713)644-2290. They were able to cross reference the Texaco Hydraulic Fluid that met Univis J13 to MIL-H-5606A.
There are several manufacturers of aviation hydraulic fluid that meets that MIL number. Falcon Crest Aviation Hydraulic Oil 15 is listed as the equivalent of Aeroshell or ROYCO 756E, which is MIL-H-5606A. I bought a quart can of the Falcon Crest Hydraulic Oil 15 for $6.01. The color and smell are the same as what is in the reservoir on the pump.