Sundowner 23 student pilot reported inflight fuel system malfunction resulting in an off-airport landing.

Narrative

I and my CFI took off of ZZZ1 in a Beechcraft Sundowner C23 heading towards ZZZ2 to practice for my check ride. Once establishing contact with ATC we were advised to redirect towards ZZZ3 then to ZZZ2 which we did and were in contact with the temporary tower set up at ZZZ2. After we landed and took off towards ZZZ4 the 30 minute timer went off notifying us to change tanks. I switched on the fuel pump and an instant drop in RPM occurred. While I was on the controls establishing the proper glide rate; my CFI went through troubleshooting the issue and was able to gain temporary power for moments before the RPM would drop once again. While in contact with ATC we were notified of a local private airport; ZZZ. My CFI assisted in guiding the plane towards where the airport was presumed to be. While unable to locate the airport we found a local field and due to the low altitude my CFI took controls and landed the plane.Prior to takeoff I did the pre-flight inspection and called for a full refill of the tanks and during fuel sumping post fill up of the tanks I visually confirmed full tanks; and slight fuel was spilled on both wings during the check. During the flight we had three different timer's checking when to change the tanks which were a personal timer on my phone; the flight timer within the transponder; and the fuel tank timer within the Avidyne GPS system onboard which were complied with changing the tanks every 30 minutes. Post landing in the field; a visual inspection of the tanks showed the left tank being almost empty; and the right wing being ~3/4 full with blue staining on the right wing.Personal annotated times were XA:50 for takeoff; and XC:44 for landing in the field granted time recorded would of been post landing within ~5 minutes so earlier time is to be accounted for. HOBBS recorded a total of 2.1 hours of flight time with a 5 minute grace time indicates a likely startup of XA:32.