From my understanding, the EGR solenoid is basically an override to force the EGR system to OFF (by cutting the vacuum between BPT and EGR valves) during certain conditions like idle or high rpm. The BPT valve controls how much the EGR valve opens based on exhaust pressure. According to MY1PATH, that "exhaust pressure" line is actually the intake manifold vacuum. I can't see where that "exhaust pressure" hose goes in the diagrams so I will have to look. Will the manifold vacuum decrease with less back pressure in the exhaust? I already looked at that Wikipedia article but it mentioned nothing on back pressure transducers. Going from a 1.875" OD pipe (stock diameter) to a 2.500" OD pipe is a very big difference in pipe diameter.
EDIT 1: OK I checked it out today, the exhaust pressure line on the BPT valve is connected right where the EGR tube is, so it does indeed respond to the back pressure in the exhaust. Also, I noticed that the air filter in the valve was missing. The BPT controls how much the EGR opens based on the intake manifold vacuum, which it receives in the top port and shares with the EGR valve, and the exhaust pressure, which it receives in the bottom port. Basically, if my understanding is correct, the BPT valve uses the exhaust back pressure to modify (or reduce) how much vacuum the EGR valve receives, which determines how much the EGR valve opens. So in a case where there is too much back pressure built up, for example during a high load situation, the BPT valve releases the vacuum to the EGR valve to close or reduce the EGR valve to gain more power. In other words, the BPT valve is there to create a vacuum leak, which is why it should have a filter, to disable the EGR valve for more power.
If the BPT valve does not operate properly, for example if the diaphragm is torn or the valve is damaged, it is like having a vacuum leak to the EGR valve, which will cause the EGR valve to never open resulting in no EGR operation. On the contrary, if the BPT valve never opens, from less back pressure for example, it's like the valve does not exist. The BPT valve can be bypassed by disconnecting the small vacuum hose that's on it and plugging it; this is the hose that goes from it to the EGR valve and the override solenoid. Then the EGR valve will be controlled only by the intake manifold vacuum and the override solenoid but I have no idea if that may cause issues at certain speeds and/or loads.
EDIT 2: I think to test the EGR operation, I would have to connect a vacuum gauge to the "vacuum signal source" and see how much vacuum there is. If there is at least some vacuum then the EGR is operational and if there isn't any then the EGR system is non-functional.
EDIT 3: To disable the EGR valve operation, just yank the little hose going to it and put caps on the EGR valve and the hose. Or you can even pinch the hose off with a clothes-hanger and leave it pinched. To disable the EGR you have to pull the vacuum hose that goes to the top of the solenoid, that's where the manifold vacuum is.