Can non touch home button from iPad Gen 5 work on iPad air

I bought iPad Gen 5 digitizer with home button and used on my iPad Air 1st Gen. The touch screen works but home button does not work.

the eBay seller told me the non-touch home button for iPad Gen 5 is not compatible with iPad Air. But I see other sellers list the same product for both models.

I am wondering if it is indeed non compatible or the one I received might be defective.

my old home button and cable are both broken so cannot reuse them