Manual transmission clutch hydraulics

On a DeLorean with a five-speed manual transmission, the clutch operating system is a hydraulic system which consists of a reservoir  PN 106759 (mounted just to the side of the fuel filler neck behind an access panel), a master cylinder PN 100462, a hydraulic flexible line PN 108637 that connects between the master cylinder and slave cylinder PN 100843 (mounted on the transmission itself).
 Several failures can occur in the clutch hydraulic system. 
1 - Either of the cylinders can leak which will cause the system to be inoperative. 
1A - Master Cylinder - When the master cylinder itself leaks, it actually leaks into the foot well area of the driver’s side of the car, so to identify that, simply kneel down outside the car and shine a flash light up to the right of the gas pedal on the firewall; you will see the push rod for the master cylinder.  Look at the push rod where it goes into the cylinder you can see the boot. If there are any signs of seepage there, you can see a line of where the fluid may have run out and down onto or under the driver’s side floor carpet. See Photo 1A. 
Photo 1A Master Cylinder inside car
1B  - Slave Cylinder - If the slave cylinder is leaking, checking it with the engine cold and not running, by laying across the top of the engine and locating the slave cylinder in the valley of the "V" of the engine. You can get more access this way by disconnecting the engine cover stay and opening the lid farther. Peel back the dust boot, and if it’s wet behind the dust boot, that’s an indication that the cylinder is leaking. This can also be inspected from under the car See 
Photo 1B)
Photo 1B Slave
2 - If the original black plastic flexible line is still in place, hard shifting or gear clash when hot may be noted. This is caused by swelling of the plastic line when hot, which leads to incomplete release of the clutch. This can also cause difficulty engaging first or reverse gear when stopped. If a driver has attempted to force the shift, particularly in to second or third gear, internal transmission shift linkage parts may be damaged. This can also place extreme loads on the gear synchronizers when shifting. The fix for this is to replace the original line with a braided stainless clutch linePN 108637.
See photo 2.  If the flexible line from the master cylinder (visible just inside of the rear of the left front tire) is black plastic rather than braided stainless, it is original and should be replaced no matter what.
Photo 2 - Braided Clutch Line-Viewed from behind left front tire. The original black line will be in the same location but is shiny black plastic.
3 - There is also a rubber hose PN 106753 and two clamps PN SP10830 that connect the reservoir PN 106759 to the master cylinder. This hose can fail with age and the fluid will leak out just behind the left front tire of the car. This hose may be accessed by removing the cover inside the luggage compartment, just below the gasoline filler. See Photo 3
Photo 3 - Reservoir/Hose. 
NOTE The hose in this photo is leaking (sweating) and should be replaced. 
HYDRAULIC FLUID: The fluid in the clutch hydraulic system is specified as DOT4. This is probably to maintain uniformity with the brake system, where DOT4 is necessary for the heat levels involved. DMC Recommends Castrol GT-LMA Brake fluid only. 
DO NOT use silicone brake fluid in clutch hydraulic systems. It is slightly more compressible (and subject to air bubbles) which could cause the same problems outlined above attributed to the plastic clutch line. 

Written by Stephen Wynne with edits by James Espey. DeLorean Motor Company (Texas)
Revised 8/4/2016 DAS added details and links, added photos.