Can a retail employer require a part time employee to be "On Call" and make themselves available to work?

Short answer is "yes". Whether or not you must be paid for the on-call time depends on the extent to which your personal activities are restricted.

Thanks for the response,

Can the employer require the part time employee to find someone else to cover for them?

Thanks again

I hear about this a lot and, although I don't think it should have to be the employee's responsibility to find a replacement (that's what supervisors and managers do), it is not illegal to require it.