You will only get “other” as a reason for your return when the package was shipped and/or returned via USPS.
Private carriers such as UPS or FedEx will always have a tracking number with a history explaining the reason for return.
A lot of times when the US post office returns items, they do not specify a reason for return on the package because they probably do not know the reason themselves. This is most common for international returns (which are handled by other postal systems as well besides USPS) and may affect some domestic packages as well (depending on which USPS channels the package when through).
Unfortunately, there is no way to get additional information from the USPS as far as the reason for return is concerned.