Yes the blower works fine and so does the heater.

 

The 97 AC/Heat wiring diagram is AFU and I can't make sense of it, but try this (based on what how later XJ AC systems work):

Using a digital Ohmmeter -

Disconnect the battery ground cable,

Place the AC/Heat mode selector off,

Disconnect the Low Pressure Switch,

Looking at the Low Pressure Switch connector, probe the right pin socket (#2) with the meter (+) probe and with the (-) probe to chassis or engine ground structure. You should read near infinity,

Place mode selector in an AC position,

Repeat meter probe positions, you should now read continuity to very low resistance.

Jumper the Low Pressure Switch and disconnect the High Pressure Switch,

Repeat same procedure as for the Low Pressure Switch, you should read continuity to very low resistance.

If you don't read continuity when reading the Low Pressure Switch with the mode selector in an AC position there is an open between the mode selector and the Low Pressure Switch Connector. If you don't read continuity when reading the High Pressure Switch, theres an open between the Low Pressure Switch and the High Pressure Switch connector.

If all readings are good, there may be an open in the AC Select ground circuit between the High Pressure Switch and the PCM.

Do these tests and see what you find.

 

Will do thanks.

 

Correction made to post 17.