Frequency is 8hz I only found 2% and I'm willing to go the extra part count for 1% tolerance.
What value...
1-2uf is fine
...value can vary...
Its a misunderstanding, I would accept any range 1-2uF so long as that value is 1% ideally it would be 1uF but not critical.
...Measure it's value...
Okay, so get a 1.5uF 20% capacitor. Measure it's value with a precision of 1%. Say it measures 1.62uF. You now have a 1.62uF capacitor with a tolerance 1%, which satisfies your requirement.
Besides temperature, humidity is a relevant drift factor. If you study manufacturers application notes, you'll find that among standard capacitor dielectrics, polypropylene gives best overall drift performance. 1% seems feasible.
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