On the 1996 Toyota Tacoma, the P1300 is a straight forward code pointing to a fault with the Igniter. This is also referred to as the Ignition Control Module. This module is responsible for sending spark at the correct time. So when faulty or intermittent, it can present with the poor idle. Carefully inspect the electrical connector and wire harness for any loose, broken or damaged wires. If the visual inspection checks ok, replacing the Igniter should solve the problem.
The p0420- this IS the code for a failing Catalytic Converter, HOWEVER, when there is a cylinder misfire, this will QUICKLY effect the Converter and set the p0420 code. If this code returns after the Igniter is replaced and there are no more misfire symptoms, then unfortunately, the cylinder misfire may have damaged the Converter and it will need to be replaced.
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