Theory:

GERRARD: And this is where dodging has brought you?
 
INTRUDER: It brought me to Aylesbury. That’s where I saw you in the car. Two other people saw you and started to talk. I listened. It looks like you’re a bit queer — kind of a mystery man.
 
GERRARD: A mystery which I propose to explain.
 
INTRUDER: (disregarding him) You phone your orders and sometimes you go away suddenly and come back just the same. Those are just the things I want to do. Hearing about you was one of my luckiest breaks.
 
GERRARD: Apparently you haven’t the intelligence to ask why I am invested in this cloak of mystery.
Explanation:
 
After listening to the intruder's crime story, Gerrard asked the intruder whether he reached Gerrard's cottage while running from the police. So, the intruder began to explain how he came to be in the town of Aylesbury while fleeing from police officers.
 
Cops - chasing the intruder.jpg
Cops - chasing the intruder
 
And it was there that the intruder happened to see Gerrard in a car. Also, he overheard few local people talking about Gerrard, which revealed Gerrard's strange, mysterious life. And the intruder planned to exploit the situation to flee from the cops.  Aylesbury is the county town of Buckinghamshire, which is located in the southeast of the United Kingdom.
 
Gerrard told the intruder that he was about to explain the mystery that surrounded him to the intruder earlier. But, the intruder, on the other hand, did not pay attention to Gerrard's comments and did not give him the opportunity to speak. The stranger continued speaking despite Gerrard's proposal. He informed Gerrard that he would place orders over the phone, then go without seeing any tradespeople and reappearing unexpectedly, indicating Gerrard's irregular routine life.
 
The only thing the intruder had to do was phone tradesmen and he didn't even have to meet them, according to the intruder. The intruder saw this as an advantage, claiming that learning about Gerrard was the luckiest thing that could have happened to him because Gerrard's neighbours did not know about him, allowing him to take advantage of it. He wouldn't have to meet people as Gerrard did, so no one would suspect him, and cops may miss him entirely.
 
But, Gerrard was smart enough to divert the intruder. He commented the intruder was not intelligent enough to guess why Gerrard was living such a life of mystery. Gerrard's reasonable query began to occupy the intruder's thinking.
 
While the intruder felt he was lucky to learn Gerrard was a mystery person, Gerrard's mysterious lifestyle was about to save himself, so it looks Gerrard was fortunate in the end.
 
Meaning of difficult words:
 
S.No
Words
Meaning
1.
DodgeTo move quickly and suddenly in order to avoid somebody
2.
Mystery Something that is difficult to understand and explain
3.
Propose To suggest something
4.
Luckiest break Fortunate and unexpected turn of events
5.
Cloak To cover or hide something
Reference:
National Council of Educational Research and Training (2006). Beehive. If I Were You - Doughlas James (pp. 138-144). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.