Depending on stability and availability of your thiol, did you try to heat a solution of the thiol with thymine, e.g. in EtOH, in the presence of an acid catalyst?
Another possibility might be to use S-alkyl isothiourea and build the thymine ring.
You can use S-alkylation with thiotymine as a substrate (2-tho or 4-thio depending on your target compound). This type of linker is not stable in acidic conditions.