Unfortunately with strips, they can be wildly inaccurate. Higher chlorine levels can bleach out the test strip, making it look like you have none! So you actually may have lots. Many old post about that - people finding when they get their test kits, that the strips were completely lying about no chlorine.
Keep adding a gallon a day until your kit comes in. That is a barely keep up level, so won't drive things higher (if they are high). And will also keep any bad things at bay, even if you later test low.
The SWCG dial doesn't regulate strength directly. It tell the cell to make CL for 70% of the time it is getting power, and turn off 30% of the time. (The actual time for the on/off cycle depends on the brand). So even if your test strip can register something, if you are testing during one of the off portions....
Rarer, but one can suffer from having Ammonia in the pool. It consumes Cl extremely quickly, and takes a very large amount of liquid to get rid of. It is caused by bacteria breaking down the CYA over a longish period (winter). Typically one would see either no CYA at all after opening, or the CYA levels you do see would fall noticeably over time (CYA amounts are usually very consistent in a pool, unless you add lots of water or add more CYA). But, you guessed it, you need a very dependable test kit to diagnose.
So until you get the kit, the prudent thing to do is just keep adding daily.