I have tried this and it worked for me.Gel pens have a long tube like structure commonly called the 'refill'.The tip of the tube is occupied by the nib.Many a times I have seen that the nib stops working as it gets easily damged.
This nib can be removed and only the plastic tube with ink is left.Note here,that the nib not just only mean the metallic part but also the plastic casing holding it.
Use nib of empty refill for replacement
You :- You can remove the nib of the non working gel pen you are talking about with your hands or by some sort of instruments by tilting it left and right and slowly pulling it up.It is better if you do it in a washbasin.Also remember to hold the tube horizontal,for the viscous ink wont flow away.Now take another empty refill,take out its nib in the same way and insert it in the desired refill.Before that,make sure to check the compatibility of the nib of this empty refill with the one you opened.
You can use alcohol as it is a good non polar solvent
Alchol :- Alcohol is a good non polar solvent and you can easily dissolve ink in it.So, you can open the nib like I mentioned above,use a dropper and put 1-2 drops of alcohol on it from the tip where there is ink.Shake the refill after closing the nib.If the ink were clogged,it would flow smoothly now.