I have this exact issue on my Road Bike ('98 Raleigh R700 purchased new March 1998). This is Ultegra 9 speed and only the rear shifter does not work when upshifting to the larger rear sprocket (easier gear). This issue only occurs during cold weather (30~40°F). Once the temperatures get above 50°F the shifting improves and at 60°F there is no issue at all.
I've thought this might be cabling as I use teflon lube on all my bike - it can be sort of thick when cold.
Are you aware of the ability to access this "pawl" on my '98 Ultegra shifters? These were the first generation 9 speed with the rattling caps. Several years ago I wrote to Shimano and they sent me replacement caps that ended the rattle.