Here is a helpful article from Mr Finespanner. Replace all bushings to eliminate play in the shaft. Bushings in nylon are available from Bill Bolton. I cannot find the original article, here is a cut and paste.
DEAD SPOTS AND THE POURED BUSHING BED
or
SIX CYLINDER THROTTLE LINKAGE
REPAIR AND ADJUSTMENT
by Mr. Finespanner®©
PART ONE: REPAIR
One problem with six cylinder Healeys very often overlooked in the course of a service or restoration is the condition of the throttle linkage, particularly the bushing assemblies through which the gas pedal and linkage cross shafts pass. It’s easy to understand why these can be neglected, since the cross shaft is basically invisible on a finished car, and you can’t tell by just looking at the other bushings if they need work.
So try this test sometime: get an observer to watch the link from the manifold to the carb shafts while you slowly depress the gas pedal, and have him tell you the exact point the link begins to move after the gas pedal begins its travel. On a car with tight linkage the gas pedal should move no more than ¼” down before the carb butterflies begin to open. If the pedal travel is in excess of ½” it indicates wear or slop somewhere in the throttle linkage. If you have an inch or more of movement before the carb shafts are affected then you have a severe dead spot, which not only limits the top speed but also causes a significant lag in the throttle response. This can have a very negative effect on your ability to avoid or escape nasty traffic situations.
So what causes this dead spot? Basically, it’s a function of rot caused by heat and time. The shaft bushings are packed in a steel housing that the mounting brackets can hold. Originally the packing material was felt, which was changed to a rubber compound called “compo” on later cars. The felt, or compo as the case may be, dries out and deteriorates over time, especially in those bushing assemblies closest to the exhaust manifold. These are the bushing on the outside of the footwell where the gas pedal shaft goes through to the engine bay (Fig. 1), and the bushing on the left end of the linkage cross shaft (Fig. 2). When the packing dries out it just turns to chunky black bits and disappears, leaving the bushing flopping in the housing when the gas pedal is pressed (Fig. 3). The free play caused by the missing packing must be taken up by the bushing contacting the housing before any of the movement is transferred to the rest of the linkage. Thus the dead spot. Another more obvious slop location is the bushing on the firewall (Fig. 4) for the top linkage shaft running forward on the intake manifold. This
one is not rebuildable, but is the easiest to replace
There are a number of ways to deal with the other shaft bushings. Unfortunately, the linkage cross shaft is virtually inaccessible with the motor in place (see Fig. 5). It IS possible to get it in and out by yanking the gearbox cover and working from behind, but it’s a royal pain. So my recommendation is to tackle that aspect with the motor out if you can. The gas pedal shaft is much easier. You just take the yoke off the end in the engine bay and remove the two screws inside the footwell holding the pedal shaft bracket to get the entire pedal shaft assembly out. At that point the bushing housing for the yoke end of the shaft can be removed from the outside of the footwell. Note the gas pedal shaft has a bushing for the holding bracket (Fig. 6) as well as one for the yoke end. Now, it is possible to get replacement bushings from some suppliers. The ones I’ve seen are nice, made from Delrin and a good permanent fix. However, the Delrin bush and housing sell for around $43.00. The following is a good fix at a fraction of the cost, and even more concours. First a simple alignment tool is required. Get a tall-shouldered 3/8” bolt about an inch and a quarter long, with some flat washers and a nut (Fig. 7). Then clean out all the old packing from the steel housing and the bushing so they are both down to clean, bare metal. Rough the outside of the bushing with a file or hacksaw to give the silicone a better gripping surface Then use an RTV silicone gasket material like Permatex Ultra-Black to lay down a thick bead of silicone sealer in the housing and another around the bushing. Put the bushing into the housing and then fill in any low spots (Fig. 8). Smear a little grease on the side of the flat washer that will go against the wet silicone and then assemble the alignment tool (Fig. 9), centering the flat washers on the bushing housing and tightening the nut finger-tight. Then just set the whole deal aside to dry for a day or so. It does take a while to set up. After a day, remove the aligning bolt and let the silicone continue to dry uncovered until it is all completely firm. Scrape off any excess dry silicone from the housing and bushing bore and you are ready for painting and reassembly (Figs. 10, 11, & 12).