In these days of "multi-tasking" and providing "service above and beyond", let's not forget that PROPERTY MANAGEMENT is a specialty that requires expertise and education above and beyond general brokerage sales training.
It it not just pulling a few sheets from the lease pad in the front desk or getting sign-on authorization from your real estate forms provider, writing a lease, even just filling in the blanks, should be done with direction...from your broker, attorney or client under supervision of your broker.
If your property owner from your unsold listing has moved out of state and wants you to "manage" his home until it can be put back on the sales market, you need a property management agreement as your listing agreement is a one-time employment agreement with a short end date.
A property management agreement should be for a minimum of 1 year and possible 2 years so that you and your client can ride out any local market obstacles from the prior attempt to sell the property.
At this point, find a local property management group (NARPM.org has chapters in most major cities and most states) and there are various trade associations like your local and state Realtor associations as well as community colleges and investor groups who provide landlord-tenant and property management courses.
There are also numerous Fb groups regarding property management; however, be careful that they are not "fronts" for property management vendors who want to sell you seminars, training, franchises and convention seats.
If you know a local property manager, take them to lunch and pick their brain....ask about the landlord-tenant attorney they use, property management software (client accounting) and how they get their service vendors. Pay for lunch and ask them if you can call or e-mail them if you have any questions.
.....then you will be on the right path to becoming a Property Manager.