Tinning brass vase caps can help in obtaining a secure joint without long dwells at each joint, that risk overheating the glass.
Heat your vase cap with a torch of one kind or another. You can heat until it becomes a dull red. The quickly brush or rub (with a cloth) flux onto the inside and outside of the rim of the vase cap. Apply a little solder to the fluxed area while everything is still hot. This will tin all the areas where the flux was placed.
This method gives a strong solder to solder joint that requires much less time when soldering the cap to the rest of the lamp shade.