When you step on the toilet pedal, wht do you see? Daylight? If so it may be a "Park Model" which means it needs to be hooked up to full-hookups in order to use legally.
Although I thought park models were pretty much a thing of the 50's...it could have been modified by a PO. Back in the day, they would dig a "golpher hole" to dump into if they didn't have tanks. My guess is that you do have a black tank, but not a grey or "wash water" tank, they weren't standard until 73/74.
If you don't see daylight, it probably has a tank and it's in the back below the toilet area. There is usually an access panel in the back of your trailer to access the dump valves ~