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Like any used TT, one important inspection is looking for any signs of leaks, inside and out. Get on the roof checking for soft spots and/or cracks in any of the caulking. Inside the TT look for any stains (walls, ceiling, inside cabinets, etc.) that may suggest that moisture was present.
If the Eagle has the Filon/Fiberglass siding, look for any signs of delamination.