The basic problem is that the occupancy switch that you chose to purchase is one designed to be able to work in series with the load attached to it. If the attached load is too small (too low of wattage) the switch assembly does not get enough power to operate correctly. For the particular model you have this is on the order of 40 to 50 watts of minimum load. From a technical standpoint it kind of sucks that they work this way BUT they are designed to work in place of a simple light switch that is in in series with its load.
Your Radio Shack relay does not come close to representing a 40-50W load on the switch so the only other way is to add some additional load in series with the switch (i.e. equivalently in parallel with the relay coil). As you have come to see this is not a very satisfactory solution and some other scheme needs to be found.
The best situation in this case is to acquire the alternate type of occupancy switch as mentioned in that thread that you linked. That type of switch has a live AC lead and neutral AC lead connected to it to power the switch unit irrespective of the size of the load. A separate output connection goes off to the load you are trying to switch. This type of switch may take a little re-wiring in your garage but that should be easier than trying to wire in the kludged extra load that the current switch requires. If you choose to deploy this improved version of the switch you will be able to remove the Radio Shack relay from the installation.
To make yourself feel better about the fact that you now have an extra occupancy switch you could pick a room in your house that has a tendency to get its light left on accidentally and install the extra unit in place of its light switch. Maybe this is a bathroom the kids use or a far closet that does not get used often.
BTW
It looks like Leviton now has a whole slew of different model occupancy switches that are also designed for single pole switch replacement but have removed the minimum load requirements. These do not require a neutral wire connection but do require a GND wire connection.
Replace ballast and lamps, and for extra savings, on a four tube per bay fixture, get a 3-lamp ballast and run only three tubes.
The extra efficiency of the smaller tube plus high-frequency electronic ballast means that three T-8 tubes can put out nearly the same light as four T-12 tubes.
The ballast tends to be a lot smaller, and weigh much less than the t-12 ballasts.
![enter image description here](https://i.stack.imgur.com/Iej3U.jpg)
Wiring varies -- your ballast will have a wiring diagram. But to give you an idea, here is an example of wiring for an instant-start electronic ballast (which are easier to wire, but tend to fail bulbs faster); and a rapid-start or programmed-start electronic ballast (which often matches the old magnetic ballasts):
![enter image description here](https://i.stack.imgur.com/P8ktr.png)
For the smaller 18AWG solid-core wires in ballasts, don't use the common yellow/red wire nuts. Use blue wire-nuts, or for instance, push-in wiring connectors such as Gardner Bender PushGard, others are available... make sure the size is correct for 18 AWG wire.
![enter image description here](https://i.stack.imgur.com/uWmej.jpg)
You can reduce number of bulbs, since T8s are brighter. A complete building rewire from four T12 to three T8 tubes per fixture eliminated 38 tubes and at 32W each, was a savings of 1216 Watts in power reduction if you only count tube elimination and not also ballast efficiency over mangetic (est. 10-15w per ballast replaced). PLUS, NO FLICKER! For someone with fast vision, not seeing 60Hz flicker in the peripheral vision was almost worth more than the power savings.
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You need to bypass the starters electrically. I leave them in place, saves having to fill the hole.