Still can’t figure out lean over run and start up issue

[1998v8]

The car is a 1998 esprit v8. I have rebuilt nearly the whole car recently but there’s one thing I still cant get. The car will start fine cold, and start fine hot, but once stated it will misfire, run choppy and sometimes die. This will only last for about 10 seconds, and as wick as a snap of the fingers the car will switch to being perfect. 
 

On throttle and driving it acts perfectly normal, until you give it more than say 80% throttle and climb above 4K rpm and then let off the throttle, the same thing happens again, and it will feel lean and choppy for 10 seconds before instantly switching to perfect again. this only happens when the throttle is released and will act fine again once I depress the pedal about 20% or so. 
 

I have changed all 10 injectors, had the ecu rebuilt, pumps and fuel lines, the filter and a complete new ignition system. As well as sensors like coolant temp, map sensor and iat. Does this sound like a bad TPS? 

 

The problem almost feels fuel related but when it comes back to life, it happens so fast I don’t know how it could be anything but electrical or sensor related. Any input would help! 

[1998v8]

When I swap a grey relay out for the circled brown relay. The pump will run continuously even with the key off, but this fixes the issue. I tried swapping in a few other brown Siemens and 1088 relays and this didn’t change anything. Only the incorrect grey relay will get the car running well so I’m not sure what my next step should be 

[LotuStuart]

You may already know all this...

The brown one may be broken. I hope you are swapping in known good identical relays in place of the brown one, otherwise you will not get anywhere!

Have you tried opening the brown one up to see what is inside? Any burnt contacts? Any melted components?

Is the brown one a "1088" relay?

If swapping in a known working one doesn't fix it, the problem is likely to be the inputs to the relay rather than the relay.

 

[fjmuurling]

Be careful with swapping relais.

The brown one has a "protection" resistor build in across the coil which kills the inductive voltage created when the coil is switched off and thus protection the driving circuit against the high inductive voltages.