NA injection pump runs rough when

I have a request from a neighbor who has a 1981 1.6L NA diesel caddy. He has a pump that was rebuilt for him about 40k to 50k miles ago. He said his pump has always started, but the idle was rough and low and , he has to give it more pedal to keep it running until it warms up; then the pump and engine runs and responds fine. After the initial cold start, the  engine starts, idles and responds fine. I told him I know nothing about pumps; but perhaps the cold start was not adjusted correctly. What else could cause the cold start problem? Thanks.   

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1982 caddy 1.6L NA running
1967 convertible bug running
1980 caddy project 
1991 2 door Jetta TD restoration in progress
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