The only realistic way to check for leaks is to fill it full and leave it at least 24 hours. I prefer a few days with a used tank and fill it right to the very top to see if there is any wicking of water under the plastic rim. It should not do that, but it can happen, and best to find out now, not the day you overfill it and find it dripping down the sides. Amazing how much water can wick out before the level drops low enough to stop it.
If it does not leak during the test, resealing is optional. If you think the old seal is worn, or if it is very soft, or discoloured, it might be worth doing anyway. If you do, you must be careful not to cut into the seal between the glass panes, but it is not that hard to avoid, just don't push too hard if you are aiming the blade straight down toward the space between panes.
I find a long handle bent scraper is easiest to use, but a very short handle one is good for corners and tight spots. Remove the top trim, it is usually not very snugly attached. Might have to run a blade through a few spots of glue or silicone, so you don't break it. Then, when you put it back, fill the channel that goes over the glass rim with silicone, and it will never 'wick' water if you overfill the tank.
Buy a box of 100 razor scraper blades, it's cheaper. They wear out fast and don't work once they are dull. Run the blade along one pane, under the seal, 'til you hit the pane of glass it's attached to. If you run long wise, it helps take off a long strip, but don't dig into the glass pane the blade corner is touching, as it can scratch, which can lead to glass cracking later on. Corners are the hardest part to get. Look at the glass under lights and at an angle to see what you missed. It will look duller than the glass.
A vacuum hose with a soft dust brush on it works great for sucking up the bits, which stick to everything once they're cut off.
You must remove every trace of old silicone, it will prevent the new from sticking. It is a pain to do and takes time. You need to be able to reach all parts of the tank without putting undue pressure on any part of it. A thick towel or something under it will pad it and prevent scratches, must be on a level surface. You'll need some plastic scrubbies, and I find filling the tank when I think I have removed all the old caulk will usually show me the stuff I missed. Either it will move in the water or look a bit whitish in the water. Check from several angles, every pane.
There isn't anything that will actually dissolve old silicone that will not also dissolve the stuff between the glass panes. Using acetone only removes grease, not sealant. There is a product that says it will remove old silicone, but as I said, it will soften the stuff between the panes too, which is not worth the risk.
But when done, by all means use something to clean the glass, as grease prevents sticking too. Windex is fine, cause you are going to rinse like crazy and refill it at least once more, before you get to fish, so any cleaner will be rinsed off. Even dish liquid will get rinsed off thoroughly by the time you are done. But avoid solvents like paint thinner, which are much harder to remove from the glass and much more toxic as well. I know some would not use any cleaners, but I find so long as I rinse thoroughly, they are not a big problem. But I don't use floor cleaners or such. Windex, water/vinegar mix, or plain dish soap liquid will clean the glass of grease and dirt and are easily rinsed off. You could use ammonia too, if you have it and can stand the smell.
I find painter's tape really helps get a nice even line, especially if you are not used to using caulk, & you'll need a caulking gun, quite cheap at hardware departments if you don't have one. Put tape down carefully, it can stretch if you pull too much, and give you wobbly lines. When you get to the first corner with the tape, lap the next row of tape over the first one in the corner, so that when you remove it, pulling it off the way you put it on will lift each corner in turn, and save some trouble. Use one of the razor blades to trim the tape in the corners so it's pretty square, to get neat corners with the caulk.
The tape must be removed immediately once the job is done, because if the sealtant begins to skin over before you take off the tape, it will stick to the tape and be removed with the tape, leaving a mess and you have to start over. I learned that the hard way
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Tape also makes it possible to go fairly fast. Depending on the silicone caulk itself, and how hot or dry or humid it is, you may only have about twenty minutes to finish once you start, before skinning over begins. Once you have the caulk in place, run a finger over it, pressing it down so that it's fairly even and not too thick. Keep a rag or paper towel handy to swipe off any gobs of stuff that build up.
You may want to practice a bit with a box, just to get a feel for how it works, before you do the glass. As you smooth the caulk, the excess is pushed onto the tape, which you then remove. If it leaves some smears, let them dry, they scrape off more easily than if you try to take them off when wet. Make sure you squeeze the caulk thinner and thinner, 'til at the edge where the tape begins it is down to nothing, or you will have bumpy edges that may lift or allow dirt under later. Learned that the hard way too.
Use only silicone that has no mildew or mold inhibitor in it. GE makes one, it's cheaper than the stuff sold in fish stores. But so long as it does not say for kitchen and bath or that it prevents mold growth, you should be fine. Silicone only.
Once you are done, let dry until you cannot smell any vinegar odour at all and the caulk is firm and not tacky anywhere. 24 hours or more. Clean the glass well, rinse really well. Then refill and leak test again, which is also a final rinse. If all is well, then you are good to go.
The removal of old caulk is by far the hardest part of this process, but resealing is not difficult to do. I advise a bit of practice with a cardboard box, for taping and sealing, it takes only a few tries to get the hang of how much to apply and how to smooth it out.