You must be sure to configure ssl certificate and key on fop2.cfg in order for latest fop2 to work with modern browsers using https. Without it it will fallback to flash after several tries. So, you can use https bug only if you configure the ssl certificates appropriately in fop2.cfg
As you say you are using latest FOP2 on Elastix 2.5, if you happen to upgrade from FOP2 2.25, then you most probably are using an old fop2.cfg in /etc/asterisk/fop2 instead of the newer one with the ssl entries in /usr/local/fop2/fop2.cfg
If that is the case, you can edit the /etc/sysconfig/fop2 file and remove -c /etc/asterisk/fop2 from the OPTIONS line so next time you start FOP2 it will read configs from /usr/local/fop2/fop2.cfg that should be the newer ones if you upgraded to 2.31.x for example.