You need to reduce the time that maintenance techs spend gathering things together for maintenance tasks. What kinds of things? Items such as special fixtures, test rigs, supplies, lights, manuals, lubricants, and tools — that aren’t likely to be in a tool pouch or on a maintenance cart — should be procured ahead of time.
For standard procedures, develop standard kits. Each kit includes items that maintenance techs normally have to hunt around for.
For example, you could set up Motor Lubrication Kits A, B, and C. Each would have a grease gun already loaded with the correct grease plus anything else needed to correctly and neatly do the job. The maintenance procedure states which kit to use for a given asset number. The tech doesn’t have to spend time locating the lithium stearate grease, only to wonder if it’s OK to just use one of the 19 tubes of calcium complex grease on the shelf (it’s not; that will destroy the bearings).
Have a dedicated person in charge of “recharging” these kits after each use.