Hi Steve,
" I was thinking more about getting the line into the overflow bottle from the expansion tank. "
No additional fittings required;
Drill a second hole in the cap, just large enough for a snug fit on the tube. Extend tube to bottom of overflow bottle/reservoir. This will give you a single tube (no additional fittings) from so called expansion tank to reservoir.
The function of the reservoir to to allow hot expanded coolant in the cooling system, to enter and then, when system cooling, be drawn back into the cooling system.
Of course you can achieve this by adding a fitting, to the bottom or to the cap of the overflow reservoir , however this adds to cost & complexity. The complexity is two additional (to what I have suggested) unnecessary potential failure points.
On another point;
The spigot/barb on the expansion tank has little clearance - making the fitting of almost any security clamp on the tube, very difficult - I double wrap security wire before twisting (do not overtighten) - works extremely well
Use Viton/Tygon tubing that wont go hard and be sure to leave enough "slack" to accomodate engine movement😈