The white comes out. When it says “wash”, ignore, or certainly, don’t use water. The clutch reservoir should be full. If its not, your clutch pedal will be on the floor, or very little pressure from then pedal. Top off with brake fluid.
When cold, the Mk1 1st to 2nd is stiff; it varies from car to car. Mine slices like a SMLE, but maybe I’m used to these after 20+ years…
Changing the gear box oil sometimes helps, especially to a motorsport grade, like Redline. Sometimes it doesn’t. If you are having the il topped off, something is wrong (ie a leak).
In addition, you have the turret oil; a seperate reservoir accessible from within the car. Around 90mls of gear oil lubricates the shift mechanism, and is contained by a rubber boot. More than likely, your is split, and doing nothing except let crud in. Remove the gear knob, centre console (5 screws), unplug the power window block, take off the bits of insulation.
There is a upper boot. Ths will be in peices. Some 10mm bolts hold it in. Remove, throw away. There you will see the gearbox turret. ake sure the shifter is in neutral. Remove the 3 10mm bolts, and with a cloth to hand, remove the gear lever, with the boot attached. Remove the old boot, and fit a new one. use a turkey baster or syringe to get out as much oil as possible. I usually do a few changes to get it clean. Same oil as the gearbox. Dn’t brim it with oil
Someone elses instructions and photos:
https://www.miata.net/garage/trans/18.htm
All the bits you need:
https://www.mx5parts.co.uk/gearlever-shift-boot-package-genuine-mazda-mk1-25-p-1111.html
Replacing the bushing on the end is highly recommended.