Respectfully, I disagree, having studied these bikes' electrical systems for years to better design and manufacture a few electrical parts for several Honda models, including some CT's.
All years of the Honda CT70 (Mini Trail 70) from K0-onward, have AC magneto ignition. A stator winding generates AC power for the ignition.
The engine will run very well, regardless of whether a battery is present or not. Newest ones have AC-powered CDI, no battery needed to run the engine.
NOTE: a missing or unchargeable battery will allow the battery charging Voltage to rise too high, easily blowing the stop light and dash lamp bulbs.
All years of the Honda CT90 (Trail 90) have battery-powered ignition, and thus this bike requires a charged battery to start and run properly. Ditto for the S90 street bike, just about the same engine/wiring.
All models of Honda CT110 have AC magneto ignition. The engine will run very well, regardless of whether a battery is present or not.
On all CT models, the spark plug boot is prone to failure. Many incorporate a noise-supression resistor inside, which will burn open and fail.
The spark plug wire is comprised of several strands of solid wire. These wires often erode away where the spark plug boot threads into the wire. Unscrew the boot and inspect for blackened or missing strands. Unless you see bright, shiny wire strands, trim a tiny bit off the end of the wire until clean conductors are showing, then thread the spark plug boot back on.
The CT70 points and condenser may need service. Located under the flywheel, the rubbing block on the points will wear down after a while, closing the point gap. In this case, replacing the points will usually restore good spark.
The CT70 ignition coil must be well-grounded to the chassis... likewise the engine must be well-grounded to the chassis. These connections tie the coil ground, coil output, ignition power, and spark plug ground together. The engine mounting bolts and the engine-to-frame bosses will corrode over time and the spark can weaken. Adding a ground wire between frame and engine, or servicing the chassis, will resolve this.
The wiring itself may be corroded, crushed, mangled, disconnected, partly shorted, or just worn out. Same for the brass-plated terminals.
One of my illustrations covers the CT70 K0 ignition switch, which remains similar throughout the model run.
The CT70 ignition switch grounds the AC magneto coil power, to kill the engine. The switch can become contaminated with crud after a while. Disconnecting the Black wire from the ignition switch will prove whether you have a bad switch. Note: you cannot kill the engine if the Black wire is disconnected from the ignition switch. This is just for testing.
The $7 "Radio Shack" full-wave rectifier upgrade does not apply to the CT70, only for some models of CT110, and for all models of CT90. There is a way to make a 3 dollar half-wave rectifier for the CT70, similar to the way you make one for a C70 Cub.
Jon