Did Deborah and Gideon Judge Together?
Yes, according to http://www.bible.ca/archeology/bible-archeology-exodus-route-date-chronology-of-judges.htm
We can prove that Deborah and Gideon judged at the same time. After each Judge the narrative tells us there were two periods of 40 years where the land had rest. Most view these as two different sets of 40 years which they add up to 80 chronological years. However, these two periods of 40 years of rest are in fact the same period and amount to a total of only 40 chronological years. Therefore we match the 40 years of rest of Gideon (8:28) with the 40 years of rest of Deborah (5:31) and it creates a close harmony with the 300 years of Jephthah in Judges 11:26.
By lining up the two 40 years of peace, we very nicely splice the end of "indivisible unit 1", with the beginning of "indivisible unit 2".
This shows us that Israel was being oppressed in the north by the Canaanites at the same time the Midianites were crossing the Jordan and raiding the crops of central Israel, then returning transjordan.
Deborah's battle was at Mt. Tabor and involved 10,000 men from the tribes of Naphtali and Zebulun: "the God of Israel, has commanded, 'Go and march to Mount Tabor, and take with you ten thousand men from the sons of Naphtali and from the sons of Zebulun." Judges 4:6.
Gideon's battle started in the valley of Jezreel, then moved transjordan far east of the Jordan and involved a specialized army of 300 from Manasseh, Asher, Zebulun, and Naphtali: "the Midianites and Amalekites and the sons of the east ... camped in the valley of Jezreel. ... Gideon ... called together to follow him: Manasseh, Asher, Zebulun, and Naphtali, and they came up to meet them." Judges 6:33-35.
The critical link between Deborah and Gideon is in the tribes who fought and the tribes who refused to fight. Deborah started judging 13 years before Gideon and chastised the region of Gilead, and the tribes of Dan and Asher because they would not join in the battle: "Gilead remained across the Jordan; And why did Dan stay in ships? Asher sat at the seashore, And remained by its landings." Judges 5:17. She praises Zebulun and Naphtali for joining the battle: ""Zebulun was a people who despised their lives even to death, And Naphtali also, on the high places of the field." Judges 5:18
When Gideon (from the tribe of Manasseh) started judging 13 years later, the same tribes fight and the same tribes refused! Gideon comes to two towns in Gilead (Succoth and Penuel) and asks the leaders for food to feed his army of 300 and they both refuse. (8:5-8) Gilead had previously refused Deborah's request for help at Mt. Tabor: "Gilead remained across the Jordan" Judges 5:17. So this was the second time Gilead had refused to fight for their brethren. After Gideon destroys Midian, he returns and destroys the town leaders of Gilead (Succoth and Penuel). A kind of "two strikes and you're out" policy with God. Later Gilead would redeem themselves under Jephthah, who himself was a Gileadite who saved themselves from the Ammonite oppression. Perhaps still not that noble, since they were merely defending their own home turf from the invasion of the king of Ammon. Good thing the Gileadites had no French genes in them, or else they would have just surrounded to the Ammonites and expected the other tribes to liberate an fight for them!
So we can prove that Deborah and Gideon Judged at the same time because they same two tribes (Zebulun and Naphtali) willingly supplied valiant warriors and the Gilead refused both of them to fight. This is an enormous key to unlocking the chronology of Judges!
Since Deborah and Gideon judged at the same time, then the 40 years of peace that followed both are identical and should be laid upon one another in chronological terms.