How did Old Testament saints show they were focused on God’s promises even though they did not know when or how their Redeemer/Messiah would appear? I am preparing a message on the importance of eliminating distractions and making Christ and His crucifixion our focal point.  These New Testament Scriptures illustrate the point:

For I resolved to know nothing while I was with you except Jesus Christ and him crucified (1 Corinthians 2:2).


As Jesus and his disciples were on their way, he came to a village where a woman named Martha opened her home to him. She had a sister called Mary, who sat at the Lord’s feet listening to what he said. But Martha was distracted by all the preparations that had to be made.  She came to him and asked, ‘Lord, don’t you care that my sister has left me to do the work by myself? Tell her to help me!’  ‘Martha, Martha,” the Lord answered, ‘you are upset about many things, but only one thing is needed.  Mary has chosen what is better, and it will not be taken away from her’ (Luke 10:38-42).

When I preach and teach, I like to use the Old Testament Scriptures to illustrate New Testament truths.
I am looking for Old Testament examples of men and women of faith who single-mindedly focused on God and His promises and who eliminated all worldly distractions in their desire to please God.
I would start with Deuteronomy 6:4-9 as the ground upon which to build your thesis

Hear, O Israel: The LORD our God, the LORD is one. You shall love the LORD your God with all your heart and with all your soul and with all your might. And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes. You shall write them on the doorposts of your house and on your gates. 

What God has said is to be held front and center of all living, doing, thinking, and speaking.  Following this there are many exhortations to neither turn from the commands of God to the left or to the right such as Deut. 5:32, Joshua 1:7, and Proverbs 4:25-27.
As the saints of old were commanded to place the Word of God as their focal point and compass so now we current saints are to fixate upon the Word made flesh and lifted up.  We are to fix our eyes upon Jesus, cast down imaginations and every high thing that exalts itself against the experiential knowledge of God, and take it all captive to obey Christ.  Moses commanded much the same:  Look to God, tear down the high places of man-made worship, obey.
I think Joshua's commission by Moses and the subsequent conquest of the promised land are fertile ground for many examples that are typical of our current experience, both good and bad.  Spend some time in prayer in Joshua.  Peace.