I'd have to see the switch (you could post a picture), but I would guess that the "opposite outside" terminal is for a neutral connection to power the pilot light. If you are measuring a fraction of an ohm between the line terminal and the load terminal when the switch is on, and essentially infinity (or in the megohms) when the switch is off, then the switch is probably operating normally.

That said, my experience is that most department store portable heaters made in the last 20-30 years were supplied with undersized switches (contacts not really designed for the load). These are often the first component to fail.

DavidR is right. In fact, a lot of these use neon bulbs which may light up even in the absence of a useful current.

Put the thing back on AC volts and measure the supposed incoming voltage.

here is a picture of the switch

Connect the ohmmeter solidly to the line and load terminals (I use clip leads for this) and work the switch back and forth a few times. Wiggle the rocker while it's on and watch the meter. If you see rock solid continuity when it's on and open when it's off, most likely the problem isn't in the switch. In that case it could be the thermostat (mechanical or electronic), heat adjustment, or nearly anything else, really. Whether you want to tackle that depends on the heater's design, your own level of comfort with electrical and/or electronic troubleshooting, and the availability and cost of spare parts from the manufacturer.

Vornado fans and heaters tend to be more expensive (and one hopes better built) than your typical Chinese dollar store specials. For me, it would probably be worth the extra effort, but I'm a stubborn old tinkerer and I refuse to junk anything I can fix. Your mileage may vary.

It is my understanding that the line (power supply in) terminal on any rocker switch is the center terminal. If so,in the picture the left terminal should be the load side of the switch since it aligns with the switch toggle when it is in the "on" position. If the switch is good should I only read continuity( a reading of zero or close to zero) when the switch is in the on position and the multimeter leads are securely connected to the line(center) terminal and the load(left) terminal?

A SPST (single pole single throw, or plain on-off) switch normally has only 2 terminals. How the NO (normally open) terminal aligns with the switch position depends on the switch's internal geometry. It won't necessarily be the terminal under the depressed side.

You should be able to figure out which terminal is which by tracing the wiring of the heater.

A SPDT (single pole double throw) switch would have 3 terminals, but there'd be no reason for the manufacturer to use one in your heater. Not that I've never seen it done (with the 3rd terminal left unused), but in this case, since your switch has a lighted handle, the third terminal is for the neutral return of the internal pilot light.

Most likely (but not absolutely certainly) the pilot light is a neon bulb. One side will be internally connected to the load terminal. The other side will be connected to the third (neutral) terminal. One side or the other will have a small resistor in series to limit the current through the bulb. You should read essentially infinite resistance across this bulb and resistor, because your ohmmeter doesn't produce the ~90vdc needed to pass a current through a neon bulb.

If the pilot light is an LED, which is possible but less likely, the ohmmeter may or may not read a resistance across it, It depends on the voltage your meter presents at its test leads, and the forward voltage of the LED. If your meter has a diode test position, you can use that to test an LED. It should read some lowish voltage (probably around 2 to 2.5v) in one direction, and zero if you reverse the test leads.

To answer your question, as I said above, IF that's the load terminal, it should read continuity with the line terminal only when the switch is in the on position.