Q: Light brown sludge in reservoir box but no loss in coolant and no sludge on oil cap or dipstick.

The sludge might simply represent cooling system contaminants. There are tests that a mechanic can perform to identify the material, that is determine if it is really engine oil. However, based on your description the contaminants are not likely to be oil. It it were oil, to answer your question such contamination is often caused by a break in the cylinder head gasket(s). In that event, the cylinder heads would have to be removed but it is not always just a matter of replacing the gasket(s) because sometimes the head or block will have to be machined to make those parts flat enough to apply a new gasket. That is, sometimes, the head gasket(s) will fail due to warping of the sealing surface. In any event, you can have the car inspected and get a conclusive diagnostic if you request a cooling system leak/contaminant inspection. If you request that service, the responding certified mechanic will get this taken care of for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic because we want you to make the most of your repair dollars and help you to get the best possible results.