On an AC transformer, the "reverse" switch merely interrupts the current flowing to the track momentarily. It does no more than turning the track power off and then on again.
The actual reverse unit, or "e-unit," is in the locomotive. It is basically a switch that cycles one position each time power is applied to the track. Because this switch changes position only on power up, to operate it, you have to cut power to the train and power it up again. That is what the "reverse button" on the transformer does.
The locomotive reverse unit has a lockout lever, or a sliding lockout switch. The lever is found on locomotives where the reverse unit is an electromechanical switch; for whatever reason, this lever is always made of nickel plated metal. The slide switch is found where the reverse unit is a circuit board. In both cases, the lockout prevents the reverse unit from changing position when power is applied, so the train will maintain the direction it was last moving in before you threw the lockout switch, even after a power interruption.
Locomotive reverse units are broadly divided into three-position (forward-neutral-reverse) and two-position (forward-reverse). The modern ones with the electronics are all going to be three-position. For the older type with the nickel-plated lever, one way to tell which is which is to look at the slot the lever rides in. On the two-position, the slot is cut in an arc. On the three-position, it is straight.
There are some low-end engines which have no reverse unit at all. In these, the reverse lever on the engine actually changes the direction. It looks the same as a two-position electrical reverse, so the only way to know for sure is to do your research.
The Lionel Scout (I mean a Scout from the postwar period, not a modern remake) has a two-position reverse, but internally it is a totally different animal than the others. Too much different to explain here. You can identify them by a stubby, thick lever (almost always black fiber or plastic) in a straight slot cut fore and aft (not side to side) in the top center of the locomotive casting. All Scouts are small steam engines.
A common problem on the three-position type with the nickel-plated lever is that the reverse unit does not cycle when power is interrupted and re-applied. On these, if you listen, there is a metallic "click" sound when power is cut--it is the sound of the electromechanical reverse unit moving to "home" (literally, a plunger falls by force of gravity). If it fails to do this, then the direction will not change when power is re-applied. This is what people mean when they talk about a "sticky e-unit". There are many posts and magazine articles about how to fix a sticky e-unit. Squirting it with tv-tuner / electronics cleaner is usually one of the first things you try.
Hope that helps!