Hi Blendin_Blandin,
For HTTP health checks you can do the following:
enable 'ssl' on the backend server
Http check method : HEAD
Though i would probably set a very low check frequency (once a minute or so.?.) or maybe not check at al..
As for the certificate, as your passing the traffic with mode tcp so haproxy doesnt need any additional settings there, a valid certificate needs to configured for the webgui though for the name your typing in the browser.
Regards
PiBa-NL