Welcome to Cloudy Nights! It looks like this was your first post here.
I would (and do) use a synchronous buck-boost converter between the battery and astronomy gear when you want to regulate the voltage. Synchronous converters such as those based on the LTC3780 control chip suggested by user RaulTheRat are seamless in their regulation. You can regulate a 12 volt source to a 12 volt output if you want. They do not have a voltage dead zone like most simpler SEPIC style converters.
That said, the mount will operate fine within a voltage range rather than exactly 12.0 volts. In fact, many mounts prefer a voltage of around 12.5 to 12.8 volts as that is near the center of the range of a lead acid battery. A regular lead acid battery will start off between 12.9 to 13.1 volts after charging and slowly drop in voltage to about 12.4 volts when it is time to recharge them.
Lead acid batteries are considered 100% depleted when they reach 10.5 volts. However if you use them down that low more than a few times, they will die completely and refuse to ever take a full charge again. They should generally be drained only to about 50% or before recharging to ensure a long life. At 50% of full charge, the voltage will be about 12.3 volts.
Using a synchronous buck-boost converter allows you to regulate a changing battery voltage to a single stable voltage. As the battery slowly drains and it's voltage drops from 13+ volts to 12.3 volts or lower, the output of the converter will provide a steady voltage without dropping out of regulation due to the 1 v to 3 v dropout range.
Find a reasonably good quality synchronous converter (like those based on the LTC3780) and use that rather than random voltage dropping elements. A good synchronous buck-boost regulator can be purchased for as little as about $10 (USD). The regulator is much more effective than any simple voltage dropping circuit you might add. Adding an LED inline with yous mount will not work and will only serve to act as a fuse. LEDs generally have a maximum current rating of a few milliamps unless you use one made for high intensity lighting which is sort of contrary to astronomy use. As soon as the mount draws current for slewing (up to 2 amps), the LED will fail and open the circuit. Chokes and other simple circuits are not likely to give you what you want. Part of the problem with a simple voltage dropping circuit is that it not only works when the battery is fully charged, it also works as the battery is drained and voltage declines.
Good luck with your new mount. Use it with just the battery and have fun until you can add the regulator you want. Just be careful not to charge the battery while using it to power the mount at the same time. A charger may reach a voltage that could be close to the limits of the mount.