Before you seam seal the tent, I would reapply the DWR (durable water repellency) finish of the tent. A tent of that age, it is likely that the DWR is worn off - which happens naturally over time - and that will allow the nylon to eventually soak through. 

Here is an REI expert advice article on care, cleaning and waterproofing your tent. 

https://www.rei.com/learn/expert-advice/caring-tent.html

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