I have both a tach and speedo made by Jaeger in the early 60's. They both usually won't read anything when first moving. If I tap, really thump the tach it will eventually work. The speedo will usually start working after a few miles. What is causeing either problem and how can I fix them?
Back when I was into all things British I had Alan Davis restore/rebuild the gauges for my MGTD and convert a tach to 12 volt negative ground/electronic ignition. Spoke with him several times on the phone after working out the time differences. Reasonable cost even with shipping across the pond. Quality work. https://thegaugeshop.com/Contact-information
I don't do British stuff, but it can be fixed. Try my friend John at Deluxe Speedometer in Denver 303-629-6958 www.deluxespeedometer.com
I'd guess they have pivots like a watch and need servicing over time. I'd also imagine they are very sensitive to doing this properly, with the right cleaning and lube. Not the place for carb cleaner and WD! Probably also have delicate adjustments too. You can price replacements and servicing and determine if you are stuck with current issues, willing to get them looked after or willing to tear them apart and try based on cost and your own ability.