Seasoning a grill has no relationship to seasoning the steak or eggplant you're grilling. In the latter case, you season to add flavor to the raw food item. But when you season a cast iron grill, you're not adding flavor. It actually refers to the process of coating the grill grate with oil, then heating it, to render it rustproof and create a virtually nonstick surface. Depending on the type of grill you own, you may only need to season the grill the first time you use it and occasionally after that. And with a Weber brand grill, you may not need to season it at all.
Chefs and the cooks who know their way around a kitchen (or a grill) know how meat feels when it's raw and when it's cooked. The only way to learn this is to basically poke the steaks at different stages of cooking. Raw meat is almost squishy, rare meat is quite soft, medium rare meat resists your poking a bit, and medium meat springs back. Once meat feels firm, it's at least well done, if not completely overdone. Gently press a finger onto your steaks—being careful not to burn yourself—to teach yourself the difference.
Reassemble the grill, then turn it on to its highest temperature setting and close the hood. There may even be a cleaning level on your burner dials. After a few minutes, open the lid and scrape the grates vigorously with a non-bristle metal grill brush. One I particularly like is the $15 Grill Bristleless Scraper from Taylor. This brush has multiple surfaces and edges to attack and remove grime from grill grates. It even has a handy bottle opener.
In lieu of fully re-seasoning your grill with each use, there are simple steps you can take to maintain and care for the condition of your grates. After each use, take a moment to run the wire brush quickly over the grates to clear away any immediate drippings. The heat in this case is helpful for removal when in smaller portions and in the moment. In the same step as above, use a pair of kitchen tongs and a paper towel to coat a layer of high heat oil over the cleaned grates before closing the grill top to cool.
Check the ignition system. Turn the gas off, and test your ignition button to see if it creates a spark. If both the pressure regulator on the gas tank and the ignition system are running normally (meaning the pressure regulator is tracking and maintaining correct gas tank pressure, and the ignition system is sparking and lighting correctly), you can finish testing the grill by turning the gas back on and lighting the grill up as you normally would.