I'd be surprised if its electric on a WW, most were mechanical I believe but I could be wrong. Maybe take some pictures including the back and the two terminals you mention and post it here if you are not sure.
If its mechanical, when you set it (other than HOLD), it should start clicking away even if it isn't plugged in or hooked up. If its mechanical and it isn't clicking along, eventually reaching OFF, then it may need a bit of coaxing to get it going again or could be completely broken hence why it was disconnected in the first place. If it does click along, test the two terminals you identified with a multi meter and see if you get continuity when its on and no continuity when its in the off position.
As for the hose, in between 1 inch and 3/4 inch would be 7/8 inch. You should be able to find something like that, it seems like dishwasher discharge hoses are 7/8 ID per the link attached. Or like Launderess suggested, take it to an automotive part shop and see if they can match something up.
Another thing to note, sometimes rubber hoses need to be softened up a bit in hot water to get them to slide onto a port.
https://www.homedepot.com/p/UDP-7-8-in-ID-x-10-ft-PVC-Disposal-Discharge-Hose-T44006003/304185159
If its mechanical, when you set it (other than HOLD), it should start clicking away even if it isn't plugged in or hooked up. If its mechanical and it isn't clicking along, eventually reaching OFF, then it may need a bit of coaxing to get it going again or could be completely broken hence why it was disconnected in the first place. If it does click along, test the two terminals you identified with a multi meter and see if you get continuity when its on and no continuity when its in the off position.
As for the hose, in between 1 inch and 3/4 inch would be 7/8 inch. You should be able to find something like that, it seems like dishwasher discharge hoses are 7/8 ID per the link attached. Or like Launderess suggested, take it to an automotive part shop and see if they can match something up.
Another thing to note, sometimes rubber hoses need to be softened up a bit in hot water to get them to slide onto a port.
https://www.homedepot.com/p/UDP-7-8-in-ID-x-10-ft-PVC-Disposal-Discharge-Hose-T44006003/304185159
