In version 10+, there is FindTransientRepeat:

• FindTransientRepeat returns a pair of lists {transient,repeat} where the elements of repeat occur successively at least n times at the end of list.
• FindTransientRepeat accepts an incomplete copy of the repeated sublist in the last position
• The minimum number of repetitions refers to complete repetitions

For the examples in the posted question

lists = {{19, 6, 19, 6, 19, 6, 19, 6, 19, 6, 19, 6}, 
         {73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7},
         {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}};

we get

FindTransientRepeat[#, 2]& /@ lists

{{{}, {19, 6}},
{{}, {73, 7, 4}},
{{73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17}, {7}}}

We can define a function that processes the output of FindTransientRepeat to get the results in desired form:

Clearall[repeatsF]
repeatsF = Module[{ftr = FindTransientRepeat[#, 2], lst = #},
 If[First @ ftr === {}, {Length @ Last @ ftr, Last @ ftr}, {Length @ lst, lst}]]&;

 repeatsF /@ lists

{{2, {19, 6}},
{3, {73, 7, 4}},
{14, {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}}}

In versions 10+, there is FindTransientRepeat:

• FindTransientRepeat[list, n] returns a pair of lists {transient,repeat} where the elements of repeat occur successively at least n times at the end of list.
• FindTransientRepeat accepts an incomplete copy of the repeated sublist in the last position
• The minimum number of repetitions refers to complete repetitions

For the examples in the posted question

lists = {{19, 6, 19, 6, 19, 6, 19, 6, 19, 6, 19, 6}, 
         {73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7},
         {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}};

we get

FindTransientRepeat[#, 2]& /@ lists

{{{}, {19, 6}},
{{}, {73, 7, 4}},
{{73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17}, {7}}}

We can define a function that processes the output of FindTransientRepeat to get the results in desired form:

Clearall[repeatsF]
repeatsF = Module[{ftr = FindTransientRepeat[#, 2], lst = #},
 If[First @ ftr === {}, {Length @ Last @ ftr, Last @ ftr}, {Length @ lst, lst}]]&;

 repeatsF /@ lists

{{2, {19, 6}},
{3, {73, 7, 4}},
{14, {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}}}

In version 10+, there is FindTransientRepeat:

• FindTransientRepeat returns a pair of lists {transient,repeat} where the elements of repeat occur successively at least n times at the end of list.
• FindTransientRepeat accepts an incomplete copy of the repeated sublist in the last position
• The minimum number of repetitions refers to complete repetitions

For the examples in the posted question

lists = {{19, 6, 19, 6, 19, 6, 19, 6, 19, 6, 19, 6}, 
         {73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7},
         {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}};

we get

FindTransientRepeat[#, 2]& /@ lists

{{{}, {19, 6}},
{{}, {73, 7, 4}},
{{73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17}, {7}}}

We can define a function that processes the output of FindTransientRepeat to get the results in desired form:

Clearall[repeatsF]
repeatsF = Module[{ftr = FindTransientRepeat[#, 2], lst = #},
 If[First @ ftr === {}, {Length @ Last @ ftr, Last @ ftr}, {Length @ lst, lst}]]&;

 repeatsF /@ lists

{{2, {19, 6}},
{3, {73, 7, 4}},
{14, {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}}}

In version 10+, there is FindTransientRepeat:

• FindTransientRepeat returns a pair of lists {transient,repeat} where the elements of repeat occur successively at least n times at the end of list.
• FindTransientRepeat accepts an incomplete copy of the repeated sublist in the last position
• The minimum number of repetitions refers to complete repetitions

For the examples in the posted question

lists = {{19, 6, 19, 6, 19, 6, 19, 6, 19, 6, 19, 6}, 
         {73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7, 4, 73, 7},
         {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}};

we get

FindTransientRepeat[#, 2]& /@ lists

{{{}, {19, 6}},
{{}, {73, 7, 4}},
{{73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17}, {7}}}

We can define a function that processes the output of FindTransientRepeat to get the results in desired form:

Clearall[repeatsF]
repeatsF = Module[{ftr = FindTransientRepeat[#, 2], lst = #},
 If[First @ ftr === {}, {Length @ Last @ ftr, Last @ ftr}, {Length @ lst, lst}]]&;

 repeatsF /@ lists

{{2, {19, 6}},
{3, {73, 7, 4}},
{14, {73, 7, 4, 7, 2, 6, 7, 2, 7, 73, 9, 17, 7, 7}}}